001 a a strucure syn

8/8/2019 001 a a Strucure Syn

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THE CHEMISTRY GURU (Power notes on chemistry)

[email protected],[email protected]

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ATOMIC STRUCTURE

1

Dalton, in 1808 proposed Daltons atomic theory and according to theory matter was madeup of extremely small, indivisible particles called atoms. However the researches done byvarious scientists like J.J. Thomson, Goldstein, Rutherford, Chadwick, Bohr and others in the

later half of the 19th century and in the beginning of the 20th century have established, beyonddoubt, that atom was not the smallest indivisible particle but had a complex structure of itsown and was made up of still smaller particles like electrons, protons, neutrons etc. Atpresent, about 35 different subatomic particles are known.

Discovery of Electron Discharge Tube Experiment

We know that under normal condition of pressure, a gas is a poor conductor of electricity.However, if pressure is reduced, the gas be comes conducting, i.e. electricity starts flowingthrough the gas.William Crooks, in 1879, studied the conduction of electricity through gases at low pressure.

He performed the experiment in a discharge tube which is cylindrical hard glass tube about60 cm in length. It is sealed at both the ends and fitted with two metal electrodes as shown infigure.

Emission of light under reduced pressure 102 atm.The electrodes are connected to a source of high voltage while the tube is connected to avacuum pump in order to reduce the pressure inside it and the following observation aremade.1. Under normal pressure (1 atmosphere). Nothing is observed even by applying high

voltage of 10000 volts. This means that gas does not conduct the electric current.2. The pressure inside the tube is slowly reduced by working the vacuum pump. When

pressure is reduced to 102 atmosphere, the gas is found to emit light and colour of lightdepend upon of the nature of gas.

3. The emission of light cease when the pressure is reduced to 104 atmosphere, but thewalls of the discharge tube opposite to cathode starts glowing with a faint greenish light

called fluorescence.This experiment shows that the fluorescence is due to bombardment of the glass walls ofthe tube by the rays emitted from the cathode. These rays are called cathode rays.

+

+

High voltage

AnodeCathode

To vacuum pumpCathode rays

Emission of light under reduced pressure of 102 atm.


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ATOMIC STRUCTURE

2Origin of Cathode RaysCathode rays initially originate form the metal which constitutes the cathode. These are alsoformed due to bombardment of the molecules of the gas inside the discharge tube by thehigh speed of particles. (electrons) which are emitted from the cathode.

Properties of Cathode raysThe properties of cathode rays were studied by J.J. Thomson and co-workers based uponcertain experiments.

These are described as follows :(i) Cathode rays travel in straight line : When a solid object is placed in the path of the

cathode rays, its shadow is noticed immediately behind it. This shows that the cathoderays travel in straight line.

(ii) Cathode rays are made up of material particles : If a light paddle wheel made frommica are mounted on an axis is placed in the path of the cathode rays, it startsrotating. This shows the cathode rays consists of material particle.

(iii) Cathode rays consist of negatively charged particle : When electrical field isapplied on the cathode rays with the help of a pair of metal plates as shown in figure,Cathode rays are found to be deflected towards the positive plate indicating thepressure of negative charge.

similarly, when a magnetic field is applied, these are deflected in a direction whichshows that they carry negative charge. R.A. Millikan (1917) by its oil drop experimentestablished that electron has charge = e = 1.60 1019 C or 4.8 1010 e.s.u.

+

AnodeCathode

To vacuum pump

Cathode rays

Cathode rays cast shadow of the object

Object

+

Light paddlewheel

Cathode rays rotate light paddle wheel

+

AnodeCathode

To vacuum pump

Electric plates

Deflection of cathode rays in electric field

Deflection ofcathode rays

+


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ATOMIC STRUCTURE

3

(iv) J.J. Thomson (1897) found thatmass

eargch

m

e= = Specific charge = 1.76 108 C / gm.

(v) Cathode rays produce heating effect. When these rays are made to strike on a metalfoil, the latter gets heated.

(vi) Cathode rays produce X-rays when they strike on surface of hard metals such astungsten copper molybdenum etc.(vii) Cathode rays can pass through thin foils of metals like aluminium. However, they are

stopped if the foil in quite thick.(viii) Cathode rays ionize the gas through which they pass.(ix) Cathode rays affect the photographic plate. This is called fogging.(x) When cathode rays strike against a glass surface or a screen coated with zinc

sulphide, they produce. fluorescence (glow).

Mass of Electrons :By using the Thomsons value of e/m and the Milikans value of e , the absolute mass of an

electron can be termede/m = 1.76 108 coulomb/g. (THOMSON)e = 1.60 1019 coulomb. (MILIKAN)

m

ee =

8

19

1076.1

106.1

q

m = 9.1 1028 gm.= 9.1 1031 kg.

Mass of Electron Relative to Hydrogen :

Avogadro number , the number of atoms in one gram atom of any element is 6.023 1023

From this we can find the absolute mass of hydrogen atom 6.023 1023

atoms of Hydrogen= 1.008 a.m.u. = gm

10023.6

008.123

= g1067.1 24

But the mass of electron = 9.1 1028 g.

28

24

101.9

1067.1

electronofmass

atomsHofmass

= = 1,835 103 = 1835

Thus a H atom is 1835 times as heavy as an electron.

In other words, The mass of an electron is th1835

1of the mass of hydrogen.

An electron is a negatively charged subatomic particle which bears charge 1.6 1019coulombs and has mass 9.1 1028 gm or 9.1 1031 Kg.Alternatively, an electron may be defined as, A particle which bears one unit negative chargeand mass 1/1835th of a hydrogen atom.


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ATOMIC STRUCTURE

4Anode Rays :How are Anode rays produced ?When high speed of electrons (cathode rays) strike molecules of a gas placed in thedischarge tube, they knock out one or more electrons from it and results positive ions.

m m+ + e

These positive ions pass through the perforated cathode and appears as positive rays. When

electric discharge is passed through the gas under high electric pressure, its molecules aredissociated in to atoms and the positive atoms (ions) constitute the positive rays.

Properties of Anode Rays :(i) They travel in a straight line in a direction opposite to cathode.(ii) They are deflected by electric as well as magnetic field in a way indicating that they

positively charged.(iii) The charge to mass ratio (e/m) of positive particles varies with the nature of the gas

placed in the discharge tube.(iv) They possess mass many times the mass of an electron.(v) They cause fluorescence in zinc sulphide.

Proton (Goldstein-1886) :E-Goldstein discovered protons in the discharge. Tube containing hydrogen.

otonPreHH + +

It was J.J. Thomson who studied their nature. He showed that(1) The actual mass of the proton is 1.672 1024 gram. On the relative scale, proton has

mass 1 atomic mass unit. (a.m.u.)(2) The electrical charge of protons is equal in magnitude but opposite to that of the electron.Thus proton carries a charge+1.61019 coulombs or +1 elementary charge unit .Since proton was the lightest positive particle found in atomic beams in the discharge tube. It

was taught to be a unit present in all other atoms. protons were also obtained in a Variety ofnuclear reaction indicating further that all atoms contains protons.

Thus a proton is defined as a subatomic particle which has a mass of 1.a.m.u. andcharge +1 elementary charge unit or simplifying.

A proton is a subatomic particle which has one unit mass and one unit positive charge.

+

ANODE+ + + +

PerforatedCathode Fluorescent

Screen

Positive

Production of Positive rays


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ATOMIC STRUCTURE

5

Neutrons (James Chadwick-1932):

James chadwick discovered the third subatomic particle He directed a stream of alphaparticle He42 at a beryllium target. He found that a new particle was ejected. It has almost the

same mass (1.6741024 gm) as a proton and has no change.ncBeHe 10

126

94

42 ++

(-particle directed at beryllium sheet eject neutrons where by the electric charge detectorremains unaffected.)The assigned relative mass of a neutron is approximately one atomic mass unit. (a.m.u.)Thus, A neutron is a subatomic particle, which has mass equal to that of proton andhas no charge.

SUBATOMIC PARTICLEParticle Symbol Nature Charge Mass(a.m.u) in kg Discover

Electron 1eo or e Negatively chargedparticle

1.6 1019Coulombs or one unit

negative charge or4.8 1010 e.s.u

0.000549 9.11031 J.J.Thomson

Proton P or1H Hydrogen nucleus +1.602 1019 c orone unit positive

charge

1.00758 1.6721027 Goldstein

Neutron on1 Neutral particle Zero Charge 1.00893 1.6741027 Chadwick

Positron +1eO one unit positive

charge i.e. +10.000549 9.11031 Anderson

NeutrinoAntineutriNo

OeO Zero charge less than the

mass of electron0.00002

Fermi

Antiproton 1p Negative charge 1.00758 ChamberLain

Meson Positive (+)

Neutral (0

)Negative ()

+ve charge

No chargeve charge

273 times heavier

than the mass ofelectron.

Yukawa

Alpha Particle : Alpha particleare shot out from radioactive elements with vary speed for e.g.They come from radan atoms at a speed of 1.5 107 m/sec. Rutherford identified them to bedi-positive helium ions +2He or He42 . Thus an particle has charged +2 and mass + 4 a.m.u.particle are also formed in the discharge tube that contains helium

-Particle

Beryllium

Neutrons

Charge DetectorIndicates no charge

(-particles directed at beryllium sheet eject neutronswhereby the electric charge detector remains unaffected)


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ATOMIC STRUCTURE

6+ + e2HeHe 2

It has twice the charge of a proton and about 4 times its mass.

Conclusion :

Through particles is not a fundamental particle of the atom (or subatomic particle) but

because of its high energy

2mv2

1. Rutherford thought of firing them like bullets at atoms

and thus obtain information about the structure of the atom.(1) He bombarded nitrogen and other light elements by particles when H+ ions or protons

were produced. This showed the pressure of protons in atoms other than hydrogen atom.(2) He got a clue of the presence of a positive nucleus in the atom as a result of the

bombardment of thin foils of metals.

Thomson Model (J.J. Thomson)

Atom is a hard solid sphere, the positivecharge of the atom is uniformally distributed,the negative charged electrons are embeddedwith in atom.This model failed to explain the scattering of aparticles by heavy atoms and the spectralseries obtained even in the simplest cases.

Rutherfords Atomic Model The Nuclear Atom:They directed a stream of very highly energetic

-particles from a radioactive source against athin gold foil provided with a circularfluorescent zinc sulphide screen around it.Whenever -particle struck the screen. A tinyflash of light was produced at the point.

Rutherford and Marsden notice that most of the-particles passed straight through the gold foiland thus produced a flash on the screen

behind it.

Observation(i) Most of the -particles (99.9%) passed through the foil without undergoing any deflection.(ii) Few -particles underwent deflection through small angles.(iii) Very few (only one in 20,000) were deflected back i.e. through an angle greater than 90o.

ZnS Screen

SLIT

Source of-Particles

Gold

Foil

Flash ofLight

Rutherford and Marsdens -particle scattering

UndeflectedParticle+

+

+

+

Nucleus

SlightlyDeflectedParticle

LargeDeflection

-Particle

How nuclear atom causes scattering of-particles

Thomson model of atom


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ATOMIC STRUCTURE

7Conclusion(1) Atom has a tiny dense central or the nucleus which contains practically the entire mass of

the atom of the nucleus is about 1013 cm. as compared to that of the atom 108 cm. If thenucleus were the size of a football, the entire atom would have a diameter at about 5

miles. It was this empty space around the nucleus which allowed the -particles to passthrough undeflected.(2) The entire positive charge of the atom is

located on the nucleus, while electronswere distributed in vacant space around it.It was due to the presence of the positivecharge on the nucleus that - particles(He2+) were repelled by it and scattered inall directions.

(3) The electrons were moving in orbit or closed circular paths around the nucleus likeplanets around the sun.

What is mass number ?The total number of protons and neutrons in the nucleus of an atom is called the massnumber; it is represented by A. These elementary particles are collectively referred to asnucleons. Obviously, the mass number of an atom is a whole number. Since electrons havepractically no mass, the entire atomic mass is due to the protons and neutrons, each of whichhas a mass almost exactly one unit.Therefore, the mass number of an electron can be obtained by rounding off the experimentalvalue of atomic mass (or atomic weight) to the nearest whole number.Composition of Nucleus :Knowing the atomic number (Z) and mass number (A) of an atom, we can tell the number of

protons and neutrons contained in the nucleus; By-definition.Atomic Number, Z = Number of protons = No. of electons.Mass Number , A = Number of protons + Number Of Neutrons The number of neutrons is given by the express ion

N = A ZIsotopes : These are the atoms of the same element which have the same atomic numberbut different mass number

e.g H11 (Protium), H21 (Deuterium), H

31 (Tritium)

O-atom is also having three isotopes

OOO 188178

168

Isotopes arises because of different number of neutrons and same number of protons.Cl-atom is having two Isotopes

Cl&Cl 37173517

Isobars : The atoms which have the same mass number but different atomic number arecalled Isobars. The word isobar meaning Equally heavy

+

Rutherfords model of atom ;electrons orbiting around nucleus


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ATOMIC STRUCTURE

8iso = equal and barys = heavy For e.g. Caand,K,Ar 4020

4019

4018 are isobaric atoms . Similarly

PuandNp,U 23594235

93235

92 are isobars.

Isotones :

Atoms which have different atomic numbers and different atomic masses but the samenumbers of neutrons are called Isotones. For e.g. OandN,C 168

157

146 are isotones since

each contains eight neutrons.Isoelectronic : The species which have the same number of electrons are called Isoelectronic.e.g. O2, Ne, Na+, FSize of Isoelectronic species is inversely proportional to its nuclear charge.i.e. Order of their size is O2 > F > Ne > Na+ > Mg2+Isosters : These are the molecules of different substances which contains the same numberof atoms and the same number of electrons which leads to similarity in their physicalproperties. e.g. CO2 & N2O.Nuclear Isomers : The radioactive elements having same atomic number and same massnumber but different radioactive properties are called nuclear Isomers.

U X2 and U ZNature of Light and Electromagnetic Spectrum:According to Newton, light was regarded as a stream of particles also known as thecorpuscles of light. The particle nature could explain certain phenomena such as refractionand reflection associated with light. But at the same time, it failed to explain two otherimportant phenomena called interference diffraction. The corpuscular theory of light was,therefore , replaced by wave theory given by Huygens. In 1856, James Clark Maxwell statedthat light, X-rays, -rays and heat etc. emit energy continuously in the form of radiations orwaves and the energy is called radiant energy. These waves are associated with electricand magnetic fields and are, therefore, known as electromagnetic waves (or radiations).

Electromagnetic Wave TheoryA few important characteristics of these wavesare listed :(i) They emit energy continuously in the form of

radiations or waves.(ii) The radiations consists of electric and

magnetic fields which oscillate perpendicular toeach other and also perpendicular to thedirection in which the radiations propagate.

(iii) All the electromagnetic waves travel with the velocity of light (3.0 108 ms1).(iv) These rays do not require any medium for propagation.

Some important Characteristics of a Wave

(a) Wavelength ( or lamda). The electromagnetic waves propagate as crests and Troughs.Wavelength may be defined as the distance between any two consecutive crests ortroughs.

Crest Crest

Trough TroughPropagation of waves


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ATOMIC STRUCTURE

9Wavelength may expressed in different units such as Angstron , micron, millimicron,nanometre, picometre etc. All of them are related to S.I . unit i.e. metre as follows :1A = 1010 m; 1 micron() = 106 m, 1 milli micron (m) = 109 m1 nm = 109 m; 1 pm = 1012 m.

(b) Amplitude (a) is the height of the crest or depth of the trough and is also expressed inthe units of length.

(c) Frequency ( or nu) is the number of the wavelengths which passes through a point inone second. The units of the frequency are cycles per second (or sec1) or Hertz (Hz)1 Hz = 1 cycle per secondIt may be noted that a cycle is complete when a wave consisting of one crest and onetrough passes through a point. The electromagnetic waves differ in their frequency andwavelength.

(d) Velocity (c) of a wave is the linear distance travelled by the wave in one second. It ismeasured in ms-1.

(e) Wave number (

_

) may be defined as the number of wavelengths which can beaccommodated one cm length along the direction of propagation. The SIunit of

_ is m1.

But the units cm1 is also commonly used.

Wave number (_ )=

)(Wavelength

1

Electromagnetic spectrum :Different types of electromagnetic waves (or radiation) differ with respect to wavelength andfrequency. The wavelength of electromagnetic waves increase in the order: wavelengthsincrease in the following order :Cosmic rays < -rays < X-rays < Ultra violet rays < Visible < Infrared < Microwaves < Radiowaves.

The complete range of the electromagnetic waves is known as electromagnetic spectrum.It may be defined as : The arrangement of different electromagnetic radiations in order ofincreasing wavelength or decreasing frequency . It may be shown as follows.


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ATOMIC STRUCTURE

10

Limitations of Electromagnetic Wave Theory

PHOTOELECTRIC EFFECT

When a beam of light of sufficiently high

frequency is allowed to strike a metal surfacein vacuum, electrons are ejected from themetal surface. This phenomenon is known asPhotoelectric effect.

When ultraviolet light strikes on the metal, the emitted electrons flow to the anode and thecircuit is completed with the help of this photoelectric effect. The following observations canbe made :

1. An increase in the intensity of incident light does not increase the energy ofphotoelectrons. It merely increase their rate of emission.

2. The kinetic energy of the photoelectrons increases linearly with the frequency of incidentlight. If the frequency is decreased below a certain critical value. (Threshold frequency vo)no electrons are ejected at all.

The classical physics predicts that the kinetic energy of the photoelectrons shoulddepend on the intensity of light and not on the frequency. Thus it fails to explain theabove observations.

Increasing wave length

Decreasing frequency

10

16

10

14

10

12

10

10

10

8

-raysCosmic

10

6

Infra red Micro

waves

10

4

10

2

10

0

10

2

x-rays Ultra violet Radiowaves

Visible

v(Hz)

1024

1020 1012

108 104

1016

Violet

Indigo

Blue Green Yellow Orange red(m)

v(Hz)

V I B G Y O R

7.6x107

3.8 x 107

3.85 x 1014Electromagnetic Spectrum

ee

e

e

Ammeter tomeasurecurrent

+

Stream ofelectrons

Metal

UltravioletLight

Apparatus for measuring the photoelectric effect


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ATOMIC STRUCTURE

11

Black Body Radiation

An ideal black body is that which is a perfect absorber and a perfect emitter of radiations.

When radiant energy is allowed to fall on a carbon black or a blackened metallic surface theenergy is almost completely absorbed. When such a body is heated, it becomes first of allred, then orange, then yellow and last of all white at a very high temperature.

It emits radiations more than any other body on heating and hence it is also a perfectradiator.

Plancks Quantum theory of Radiations:Max Planck in 1900 , put forward a theory known as Plancks Quantum Theory. This wasfurther extended by Einstein in 1905. The main points of the theory are :(1) The radiant energy is emitted or absorbed discontinuously in the form of small energy

packets called Quanta. In case of light, these energy packets are known as photons.

(2) The energy of each quantum is directly proportional to the frequency of the radiationE or E = h =

c

h

Here h is a constant known as Plancks constant. Its value is 6.62 1034 J sec or3.99 1013 kJ sec mol1.

(3) The total amount of energy emitted or observed by a body is some whole number orintegral multiple of quantum i.e.

E = nh(Here n is an integer)The energy associated with Avogadros number of quanta is called Einstein energy (E).Its value may be given as

= hcNE

Thus, Plancks for the first time has given a relationship between the frequency (orwavelength) of the radiations since they have very high frequency.At the same time, microwaves and radiowaves with small frequency are regarded as lowenergy radiations.

(Explanation of Photoelectric Effect by Plancks Quantum Theory)

(i) A photon of incident light transmits itsenergy (h) to an electron in the metal

surface which escapes with kineticenergy 2mv

2

1. The greater intensity of

incident light merely implies greaternumber of photons each of whichrelease one electron. This increases therate of emission of electrons while the

e e e e eM+ M+ M+ M+

h

Photon

e

Photoelectron

(It needs a photon (h) to eject an electron with energy )m2

1 2


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ATOMIC STRUCTURE

12kinetic energy of individual photonsremains unaffected.

(ii) In order to release an electron from the metal surface, the incident photon has first toovercome the attractive force exerted by the positive ion of the metal. The energy of a

photon (h) is proportional to the frequency of incident light. The minimum whichejects the electron from the metal surface is called o. If < o , No e

will be emitted.

For higher frequencies > o a part of energy goes to loosen the electron andremaining for imparting kinetic energy to the photoelectron, thus

2o mv2

1hh += (i)

where h is the energy of the incomingphoton ho is the minimum energy for anelectron to escape from the metal and

21 mv2 is the kinetic energy of the

photoelectron.

ho is constant for a particular solid anddesignated as w, the work function.Rearranging equation (i)

whmv2

1 2 = (ii)

So w = ho here w = work function

this is the equation for a straight line ( y = mx + c) that was experimentally obtainedfigure (ii). Its slope is equal to h, the Plancks constant. The value of h thus foundcome out to be the same as was given by Planck himself.

Study of Emission and Absorption SpectraA radiation which consists of one wavelength only is called Monochromatic. Light such assunlight which consists of radiation of different wavelength is known as polychromatic. Whena polychromatic light is passed through a prism, it splits in to radiations of differentwavelengths. This splitting of a polychromatic light in to its constituent radiation is calleddispersion. It is due to bending of radiations (of different wavelength) through different angles.The pattern of radiations obtained due to dispersion, is called Spectrum.The instrument used to record a spectrum is called a spectrometer or spectrograph. It wasdeveloped by Bunsen and Kirchoff in 1859. A spectrometer consists of a prism for dispersionof light and a photographic plate to record the spectrum. The photograph of the spectrum iscalled Spectrograph.The spectra are broadly classified into1. Emission spectra2. Absorption spectra

Kineticenergyof

Photo

electrons

Frequency ofincident of light

(Kinetic energy of photoelectrons plottedagainst frequency of incident light) Fig. ii)


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ATOMIC STRUCTURE

13These are briefly explained below :1. Emission spectra. When the radiation emitted from some source e.g. from the sun or by

passing electric discharge through a gas at low pressure or by heating some substanceto high temperature etc. is passed directly through the prism and then received on the

photographic plate, the spectrum obtained is called Emission spectrum. Dependingupon the source of radiation, the emission spectra are mainly of two types :(i) Continuous spectra When white light

from any source such as sun, a bulb orany hot glowing body is analyzed bypassing through a prism, it is observedthat it splits up into seven differentwide bands of colours from violet tored, (like rainbow), as shown in fig.These colours are so continuous thateach of them merges into the next.

Hence the spectrum is calledcontinuous spectrum. It may be notedthat on passing through the prism, redcolour with the longest wavelength isdeviated least while violet colour withshortest wavelength is deviated themost.

(ii) Line spectra When some volatile salt(e.g., sodium chloride) is placed in thebunsen flame or electric discharge ispassed through a gas at low pressure

as given in fig. , light is emitted. If thislight is resolved in a spectroscope, it isfound that no continuous spectrum isobtained but some isolated colouredlines are obtained on the photographicplate separated from each other bydark spaces. This spectrum is calledLine spectrum or simply Linespectrum.

BURNER

NaCl

PLATINUMWIRE

BEAM

PRISM

Line spectrum produced from avolatile salt placed in a fame.

TWOYELLOW

LINES

5890

o

A

5896

o

A

SLIT

(a)

(b)

Prism PhotographicPlate

Beam

Slit

WhiteLight

R

O

Y

G

B

I

V

Continuous spectrum of white light


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ATOMIC STRUCTURE

14Each line in the spectrum corresponds to a particular wavelength. Further it is observed

that each element gives its own characteristic-spectrum, different from those of allother elements.For example , sodium always gives two

yellow lines (corresponding towavelengths 5890 and 5896

oA ).

Hence the spectra of the elements aredescribed as the finger prints of thehuman beings.Further, it will be discussed later thatthe line spectra are obtained as aresult of absorption and subsequentemission of energy by the electrons inthe individual atoms of the element.Hence the line spectrum is also calledatomic spectrum.

2. Absorption spectra When white light fromany source is first passed through thesolution or vapours of a chemicalsubstance and then analyzed by thespectroscope, it is observed that somedark lines are obtained in the otherwisecontinuous spectrum. These dark lines aresupposed to result from the fact that whenwhite light (containing radiations of manywavelengths) is passed through the

chemical substance, radiations of certainwavelengths are absorbed, dependingupon the nature of the element. Further it isobserved that the dark lines are at thesame place where coloured lines areobtained in the emission spectra for thesame substance.This shows that the wavelengths absorbed were same as were emitted in the emissionspectra. The spectrum thus obtained is, therefore, called absorption spectrum.

Emission spectrum of Hydrogen Whenhydrogen gas at low pressure is taken in the

discharge tube and the light emitted on passingelectric discharge is examined with aspectroscope, the spectrum obtained is calledthe emission spectrum of hydrogen . It is foundto consist of a large number of lines which aregrouped into different series, named after thediscoverers.* The names of these series and

PRISM PHOTOGRAPHICPLATE

BEAM

SLIT

H2

Gas

Line spectrum produced from alight emitted by discharge tube.

White LIGHT

NaClSOLUTION

SLITPRISM

R

O

Y

G

B

I

V

PHOTOGRAPHICPLATE

DARK LINES IN YELLOW REGIONOF CONTINUOUS SPECTRUM.

PRODUCTION OF ABSORPTION SPECTRUM

Emission or atomic spectrum of hydrogen

SERIES:LYMA BALMER PASCHEN BRACKETT PFUND

REGION:ULTRAVIOLET

INFRARED

HUMPHREY

VISIBLE FAR INFRARED


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ATOMIC STRUCTURE

15the region in which they are found to lie aregiven in fig. The wavelength of different lines In each of these series are given in Table.

Rydberg formula. Although a large number of lines are present in the hydrogen spectrum,rydberg in 1890 gave a very simple theoretical equation for calculation of the wavelengths ofthese lines. The equation gives the calculation of the wave numbers._v of the lines by the formula

_v = R

22

21 n

1

n

1. where R is a constant , called Rydberg

constant** and has a value equal to 109,677 cm1, n1 and n2 are whole numbers and for aparticular series n1 is constant and n2 varies.For example,For Lyman series, n1=1, n2 =2,3,4.For Balmer series, n1 =2, n2=3,4,5.For Paschen series n1 =3, n2= 4,5.

For Brackett series, n1 =4, n2=5,6,7For Pfund series, n1 =5, n2=6,7,8For Humphrey, n1 = 6, n2 = 7,8,9..The above expression is called Rydberg formula.

Drawbacks of Rutherfords model Instability of Atomic Structure :According to Rutherfords model, electrons areremoving around the nucleus in circular orbits. Thecentrifugal force (which arises due to the circularmotion of electrons) acting outwards balances theelectrostatics force of attraction (between thepositively charged nucleus and the negativelycharged electrons) acting inwards. This prevents theelectrons to fall the nucleus.

However, it had been shown by Clark Maxwell that a charge and accelerated particle losesenergy constantly. Electrons is a charged particle. It gets accelerated due to continuouschange in direction while moving around the nucleus. Thus an electron must, therefore, emitradiations and lose energy constantly. As the electron loses energy, its orbit would becomesmaller and smaller. Ultimately, due to electrostatic force of attraction; the electrons will fall isto nucleus. fig. since such a collapse of the atom does not take place , therefore, Rutherfordsmodel of the atom is faulty.

Failure to Explain Atomic Spectra :Rutherfords model could not explain the formation of line spectrum. According toelectromagnetic theory, frequency of radiation of a charged body is equal to its frequency ofrevolution. Since the electron orbit is continuously changing the frequency of revolution alsochanges continuously. As a result, atomic spectra of hydrogen should have been continuousrather than line spectra. This is not in agreement with the observed facts.

+

e

Continuous loss of energy by revolvingelectron


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16Bohrs Atomic ModelNeils Bohr (1913) developed a new theory of the atomic structure on the basis of quantumtheory of radiation. The main point of his theory are Bohrs Assumptions

(i) An atom consist of a dense nucleus situated at the centre around which the electrons incircular orbit.(ii) Of the very large number of possible circular orbits around the nucleus, the electron can

move only in certain fixed orbits known as stationary state. Stationary state does notmean that the electrons are stationary. An electrons keeps on revolving in the same orbitand its energy remain constant.

(iii) Each fixed or stationary state associatedwith a definite amount of energy. Thesedifferent energy levels are numbered as 1,2, 3, 4 etc. (from nucleus outward) oralternatively they are designated as K, L,

M, N shell etc.

(iv) The electron in an atom can have certain definite or discrete value of energy which arecharacteristics of that atom. In other words: The electronic energy of an atom isquantized.

(v) The electron in an atom can revolve only in those energy levels for which the angular

momentum of an electron is a whole number multiple2

hi.e.

For circular motion, the magnitude of the angular momentum L of the electron is L = mvr

Bohrs quantization of the angular momentum is L = mvr =2

nh (where n = 1, 2, 3, .)

Hence the integer n is called principal quantum number.where m mass of an electron.

v velocityr radius of orbit in which the electron movingn orbit of the electron

Electrons orbit in certain stationary states in which orbiting electrons do not continuouslyradiate electromagnetic energy. The stationary states have definite total energy. Thisassumption implies that classical law of electromagnetic radiation by an acceleratedcharge simply do not apply to an electron in it stationary orbits.

(vi) The emission or absorption of electromagnetic radiation occurs only when there is atransition of electrons between two stationary states. When an electron changes from ahigher energy orbit to a lower energy orbit. The excess energy is emitted as a photon.The frequency of the emitted or absorbed radiation is proportional to the difference inenergy of two stationary states

E = En2 En1 = hv

+

NUCLEUS

K L M Nn=1 n=2 n=3 n=4

Circular orbits (energy levels /stationary states) around the nucleus


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17

where h is the Planck constant h = 6.625 1027 erg-sec. En1 and En2 are the energies of ainitial and final state. The frequency of the photon is independent of the frequency of theelectrons orbital motion.This assumption is equivalent to that of conservation of energy with the emission of photon.

BOHRS THEORY HAS EXPLAINED THE ATOMIC SPECTRUM OF HYDROGEN ATOMBohrs theory, we have studied that the electrons are distributed in different energy levels.Normally an electron tends to be as close to the nucleus as possible or it tends to be in thelowest energy state also called ground state.In case, energy is made available to the electron from some outside source, it may absorbenergy is quantum (or quanta) and jump to the higher energy state known as excited state. e.g.in hydrogen atom,the only electron is present in the K shell (n = 1) in the ground state withenergy

1nE . If it absorbs energy equal to one quantum (hv) it jumps to first excited state with

energy equal to2n

E . Since the excited state in unstable, the electron will jump back to the ground

state by losing a quantum of energy as radiations which appear as emission spectra.

Thus,2n

E

=

===

c

1chhEn1 , In general, if the electron jumps from a particular excited

state represented as2n

E to the lower energy state (ground state) represented as1n

E , it will

emit a radiation having definite frequency and wavelength. The spectral line whichcorrespond to it will have specific colour.

Energy is absorbedwhen an electron jumps

1nE 2nE

2nE

Energy is emitted whenan electron jumps from a

E

Radiation ofFrequency

Radiation ofFrequency

Energy changes during electronic

Humphrey Series ( far Infrared)

n = 8

n = 7

n = 6

n = 5

n = 4

n = 3

n = 2

n = 1

Lyman series(Ultraviolet)

Balmer Series(Visible)

Paschen Series(Infrared)

Brackett Series

(Infrared)

Pfund Series(Infrared)

Different series in the hydrogen spectrum


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ATOMIC STRUCTURE

18From above diagram, it is evident that the Lyman series, the electrons jump from differentexcited states to n = 1. In Balmer series, they jump to n = 2 similarly, in Paschen, Brackettand Pfund series which appear in the infrared regions, the electrons drop back to energystates represented by n = 3, 4, 5 respectively. This may be summed as follows:

Name of the Spectral Series Downward TransitionLYMAN SERIESBALMER SERIESPASCHEN SERIESBRACKETT SERIESPFUND SERIESHUMPHREY SERIES

From n = 2, 3, 4, 5.. to n = 1From n = 3, 4, 5, 6 to n = 2From n = 4, 5, 6, 7 to n = 3From n = 5, 6, 7, to n = 4From n = 6, 7, 8 to n = 5From n = 7, 8.. to n = 6

Explanation for the Simultaneous Appearance of Many Spectral Lines in the HydrogenSpectrumIn study of hydrogen spectrum, we have seen the appearance of many spectral lines different

series of hydrogen spectrum such as Lyman, Balmer, Paschen Brackett and Pfund series.This appears to be some what strange because each hydrogen atom which is formed as aresult of the dissociation of hydrogen molecule in a discharge tube has only one electron. It isexpected to be excited to the some higher energy state in all the atoms of hydrogen. But inactual practice, the electrons absorb different amounts of energy and thus, are excited todifferent higher energy states depending upon the energy absorbed, since the excited statesare unstable, the electrons are to jump back to ground states. It may be noted that in thereturn journey, it is not necessary for all the electrons to follow the same route.

Maximum lines in H-spectrum when it exite to nth level =2

)1n(n when an electron

returns from n2 to n1 energy level. No. of spectral lines produced = 2

)1nn()nn( 1212 +

Some results of Bohrs Model

1. Radius of nth Bohrs OrbitConsider an electron of mass m and charge e, revolving a nucleus of charge Ze(Z atomic number and the being the charge) on a proton.Let v be the tangential velocity of revolving electron and r is the radius of orbit. Theelectrostatic force of attraction between the nucleus and electron. (Applying Coulombs law)

2

2

2

r

Ze

r

eZe=

The centrifugal force on the moving electron =r

m 2

As force of attraction = centrifugal force.

r

mv

r

Ze 2

2

2

= ormr

Zev

22 = .(i)


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ATOMIC STRUCTURE

19According to one of the postulates

mr =2

nh

= mr2

nh

Putting the value of in equation (i)

mr

Ze

rm4

hn 2

222

22

=

or 22

22

Zemr4

hn=

22

22

mze4

hnr

= .(ii)

Putting the value h, , m and e we get

cmZ

n10529.0r

28 =

o2 AnZ529.0r =

for hydrogen atom Z = 1r = 0.529 108 n2 r = 0.529 n2

2. Energy of an ElectronLet the TE is total energy of an electron in a shell, it is the sum of kinetic energy andpotential energy.TE = P.E. + K.E.

P.E.n

2

r

Ze=

K.E.n

2

r

Ze

2

1=

TE =n

2

n

2

r

Ze

2

1

r

Ze+

n

2

r2

Ze= .(iii)

TE =2

1P.E., and K.E. =

2

.E.P

Also equating (ii) and (iii), we get

22

242

hn

zme2

TE

= ergn

1072.21

2

12

=

Jn

1072.212

19=

eVn

6.13E

2

= (1 Joule = 6.2419 1018 eV)


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20

mol/calK05.23n

6.132

= (1 eV = 23.053 K cal per mol)

Energy of electron (e) in terms of K cal per mol

mol/calKn

6.313

E 2= Energy of Electron (E) in terms of kJ per mole

moleperkJn

1312E

2

=

the radius of first orbit, n = 1= 12 0.529 108 cm =0.529 108 cm= 0.529 1010 meter.

3. Velocity of an ElectronPutting the value v in equation .(ii)

22

22

hn

mZe4

m2

nhv

=

h

e2

n

Z 2=

Putting the values of n, e, h in the above equation, we get810188.2

n

Zv = cm sec1

610188.2n

Z= m sec1

for hydrogen atom, Z = 1

n

10188.2v

6= cm sec1

for first orbit of hydrogen atom, then v = 2.188 106 m sec1 for second orbit of hydrogen(n = 2), thus

610188.221v = m sec1

= 1.094 106 m sec1 No. of revolution made by an electron per second in an orbit.

No. of revolution made by electron per second =r2

v

Putting the value of r and in the above reaction

Thus the number of revolutions = 1163

2

sec10316.1n

Z

Hence the no. of revolution made by an electron per second hydrogen atom

.secn

10316.13

16=

Limitations of Bohrs Theory(i) It is unable to explain the line spectra of multi electronic atoms.(ii) It also fails to account for the multiple of fine structure of the spectral lines. Each spectral

line has been found to consist of a number of component line was observed closely in a


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ATOMIC STRUCTURE

21spectroscope of high revolving power. This suggested the presence of sub energy levelin a main energy level, which was not suggested by Bohr.

(iii) The further splitting up of spectral lines under the influence of strong magnetic field(Zeemans effect) is not explained by Bohr.

(iv) Bohr gave a flat model of the atom in which electrons are revolving in circular orbitsaround the nucleus. But at present it is believed that atom has a three dimensionalmodel. The new model leads the concept of orbitals in place of Bohrs definite orbits.

(v) This theory cannot explain the directional bonding between atoms in some molecules andthus the shape of such molecules.

(vi) Bohr theory violates Heisenbergs uncertainty principle.Heisenbergs uncertainty principle. According to this principle, the position andmomentum of a small particle like electron cannot be determined simultaneously withabsolute accuracy.

(vii) It violets the dual character (i.e. particle and wave) for an electron proposed byde-Broglie. Bohr consists electron as discrete particles and it does not take in to account

its wave character.de-Broglie concept of dual character of matter. According to this concept, an electronbehaves not only as a particle but also as a wave. Bohr, however, considered electronsonly as discrete particles.

Sommerfelds Modification of Bohrs atomSommerfeld modified Bohrs theory as follows:Bohr considered electron orbits as circular but Sommerfeld postulated the presence ofelliptical orbit also.

Dual Nature of Matter

(de-Broglie Equation)In 1924, Louis de-Broglie suggested that just as light exhibits wave and particle properties allmicroscopic material particles in motion such as electrons, protons, atoms, ions, moleculesetc. have also dual character.

In Other Words : -

All material particles in motion possess wave characteristics.

According to de-Broglie, the wavelength associated with a particle of mass m, moving withvelocity v is given by the relation.

=mv

h

p

h= (p = mv)

where h is the Plancks constant and mv is the momentum of the particle. The waveassociated with material particles are called Matter waves.


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ATOMIC STRUCTURE

22Derivation Of de-Broglie Equation

He derived a relationship between the magnitude of the wavelength associated with mass mof a moving body and its velocity.

According to Planck, photon of light having energy E is associated with a wave of frequency as

E = h (i)

where h is the Plancks constant and the frequency of radiation.

By applying Einsteins mass energy relationship the energy associated with photon of mass m.

E = mc2 (ii)

where c is the velocity of light.

Combining the above two relation in equation (i) and (ii), we get :-

h = mc2

Now, since = c or

=c

2mchc

=

h

= mc ormc

h=

The equation is valid for a photon. de-Broglie suggested that on substituting the mass of theparticle m and its velocity v in place of velocity of light c the equation can also be applied to amaterial.

Thus, the wavelength of material particles, is

mv

h =

This equation is known as de-Broglies equation.

orp

h=

where p stands for the momentum (mv) of the particle since h is constant

momentum

1

de-Broglies equation may be put in words as ----

The momentum of a particle in motion is inversely proportional to wavelength, Plancksconstant h being the constant of proportionality.


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23Significance of de-Broglie

The wave character puts some restriction on how precisely we can express the position of anelectron or any other small moving particle. This is due to the reason that unlike particleswave do not occupy a well-defined position in space and are delocalised.

The wave nature of matter, however, has no significance for object of ordinary size becausewavelength of the wave associated with them is too small to be detected.

Justification for the Dual Nature of Electrons

1. Particle nature

An electron exhibits all the characteristics of a particle i.e. It has a definite mass, energy,momentum and charge. When an electron is made to fall on a screen coated with zincsulphide, it produces a spot of light known as scintillation. It has been observed that oneelectron produces only one scintillation point. This means that the scintillation and, as

such the striking electron must be localised and not spread out like wave . Moreoverblack body radiation and photoelectric effect proves the particle nature.

2. Wave nature

Louis-de-Broglies concept of wave nature of electron was experimentally verified byelectron beam from tungsten filament is accelerated by using a high positive potential.When this fine beam of accelerated electron is allowed to fall on a large single crystal ofnickel, the electrons are scattered from the crystal in different directions. The diffractionpattern so obtained is similar to diffraction pattern obtained by Braggs experiment ondiffraction of Xrays from a target in the same way.

Since x ray have wave character, therefore the electrons must also have wavecharacter associated with them. Moreover, the wavelength of the electrons as determinedby the diffraction experiments were found to be in agreement with the values calculatedfrom de-Broglie equation.

So from this it is clear that an electron behaves both as a particle and as a wave.

Diffraction pattern

Photographic plate

Reflected rays

Nickel crystal

Incident beamof electrons

Electron diffraction experiment by Davisson and Germer


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ATOMIC STRUCTURE

24Experimental verification of de-Broglie concept

(a) Verification of wave character (Davission and Germers experiment).

The wave character of electrons was verified experimentally by Davission and Germer in

1927. They studied the diffraction of electrons by a sample of nickel crystal and found thediffraction pattern to be similar to that produced by x-rays figure, since x-rays areconfirmed to have wave character therefore, electrons must also have a wave characterassociated with them. Moreover, the values of wavelength obtained from diffractionexperiments are in agreement with those calculated from de-Broglies equation.

Thomson experiment can also be performed to verify the wave nature of electron. In thisexperiment, in place of Nickel crystal a thin gold foil is taken but similar diffraction pattern

is obtained as in case of Nickel crystal which again confirms the wave nature of electron.(b) Verification of particle character.

It is observed that when an electron strikes a zinc sulphide screen, a spot light known asscintillation is produced. Moreover, one electron produces only one scintillation point.Since scintillation is localised, therefore, the striking electron must also be localised andnot spread out like a wave. Since the localised character is possessed by particle,therefore electron has particle character. Moreover black body radiation and photoelectriceffect also proves particle nature.

Sample

x-ray Tube

Diffraction

Pattern

+

SampleSource ofElectrons

DiffractionPattern

+

AcceleratingElectrode


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25Difference between Particle and Wave

Particle Wave

1. A particle is a localised point in space. 1. A wave is delocalised(spread out) in space.

2. More than one particle cannot bepresent at a given position in a space

i.e. particle do not interfere.

2. Two or more wave can existsimultaneously in the same region of

space i.e. waves interfere.

3. If two or more particles are present in

any region, then due to non-

interference, their total value is equal

to their sum.

3 If two waves are present in a given

region, then due to interference the

resultant wave can be larger or smaller

than the individual waves

Derivation of Bohrs Postulate of Quantisation of Angular Momentum from de-Broglie

Relation

de-Broglie equation helped in explaining the Bohrs postulate regarding the quantisation ofangular momentum of an electron. Consider an electron moving around the nucleus in theform of wave in a circular orbit of radius r. The wave train of electrons may be continuously inphase or out of phase. If the two ends of the wave meet to give a regular series of crests andtroughs, the wave motion is said to be in phase as shown in Fig. If the two ends do not meetto give a regular series of crests and troughs, it is said to be out of phase [Fig.]. As evidentfrom Fig., for wave motion to be continuously in phase, the circumference of circular orbitmust be an integral multiple of number of the wavelengths otherwise the wave would interferedestructively and cancel each other and, thus, destroy itself. Therefore, by considering theelectron as wave, we automatically impose a limit to the number of orbits.

From the above discussion, it is clear that the circumference of the orbit must be integralmultiple of the electron wavelength i.e.,

Circumference = n

or 2r = n

But, according to de-Broglie equation,mv

h=

mv

nhr2 =

or

=2nhmvr

Thus, the angular momentum of the electron should be an integral multiple of h/2. In otherwords, the angular momentum is quantised. This is the same as Bohrs condition forquantisation of angular momentum of fixed energy orbits.

(a) Wave in phase (b) Wave out of phase

Representation of electron waves and orbits(a) in phase (b) out of phase.


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26HEISENBERGS UNCERTAINTY PRINCIPLE

According to Heisenbergs uncertainty principle It is impossible to measure simultaneouslythe exact position and exact momentum of a body as small as electron.

Heisenbergs uncertainty principle may be expressed as :x . p

4h

where x is uncertainty of position & p is uncertainty of momentum

x . (mv) 4

h

x . v m4

h

31

34

101.914.34

10626.6

Uncertainty Product 0.077 104 J sec per kg.

When x = 0, v =

When v = 0 x =

As uncertainty product m

1

So for macroscopic particles uncertainty product will be negligible

So Heisenbergs principle has no sense for macroscopic particles.

Physical concept of Uncertainty Principle.

The physical concept of uncertainty principle

becomes illustrated by considering an attemptto measure the position and momentum of anelectron moving in Bohrs orbit.

The locate of position of the electron we should device an instrument supermicroscope to seethe electron. A substance is said to run only if it could reflect light or any other radiation fromits surface. Because the size of the electron is too small its position at any instant may bedetermined by a supermicroscope employing light of very small wavelength (such as X-rays,or-rays). A photon of such a radiation of small has a great energy and therefore has quitelarge momentum.

As one such photon strikes the electron and is reflected it instantly changes the momentumof electron.

Now the momentum is changed and becomes more uncertain as the position of the electronis being determined.

Thus it is impossible to determine the exact position of an electron moving with a definitevelocity (or possessing definite energy).

+

Electron changesmomentum at theinstant of Collision

Photon

Nucleus


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27It appear clear that the Bohrs picture of an electron as moving in an orbit with fixed velocityor energy is completely untendable.

As it is impossible to know the position and the velocity of any one electron on account if itssmall size, the best we can do is to speak of the probability or relative chance of finding an

electron with a probable velocity.Wave Mechanical Concept of the Atom

Based upon the idea of the electron as a standing wave around the nucleus, a new modelknown as wave mechanical model was developed by Erwin Schrodinger (1927). Heconsidered the electron as three dimensional wave in electric field of the positively chargednucleus. To describe the behaviour of electron waves, Schrodinger developed amathematical equation which is popularly known after his name as Schrodinger wave

equation. The equation is 0.)E.PE(h

m8

dz

d

dy

d

dx

d2

2

2

2

2

2

2

2

=

+

+

+

. Here

(i) m = mass of the electron(ii) E = Total energy of the electron

(iii) V = Potential energy of the electron =r

Ze2

(iv) h = Plancks constant = 6.62 1027 erg. Sec. = 6.62 1034 Js.

(v) x, y and z are cartesin co-ordinates specifying direction and distance.

(vi) (read psi) is a wave function which represents the amplitude of electron wave.

Significance of .(i) It is wave function which is a solution to the Schrodinger equation.(ii) It represents amplitude of wave and describes how this amplitude varies with distance

and direction.

(iii) The Schrodinger wave equation may have different values of . All values may not besignificant. The significant values of wave function, , are known as EIGEN functions.These functions give significant values of total energy (E) of the electron. These valuesare called Eigen values.

Significance of 2The probability of finding an electron in an extremely small volume around a point isproportional to the square of the function 2 at that point. If wave function is imaginary becomes a real quantity where is a complex conjugate of . This quantity represents theprobability 2 as a function of x, y and z co-ordinates of the system and it varies from onespace region to another. Thus the probability of finding the electron in different regions isdifferent. This is in agreement with the uncertainty principle and gave a deathblow to Bohrsconcept.


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28

Concept of Orbital

According to wave mechanical approach, we cannot say simply that the electron exists at a

particular point but we talk about certain regions in space around the nucleus where theprobability of finding the electron is maximum such regions are expressed by mathematicalexpressions and are called orbital wave functions or commonly known as orbital. Therefore,the wave equation leads to the concept of the orbitals instead of well defined circular orbits.

The three-dimensional region within whichthere is higher probability that an electronhaving a certain energy will be found, is calledan orbital.

(The orbital is indicated by dotted figure representing electron cloud. The intensity of dotsgives the relative probability of finding the electron in that particular region.)

If a boundary is drawn which encloses a region where there is high probability (about 90-95%) of finding the electron, the figure obtained gives the general picture of an orbital.However, it is difficult to draw the real picture of an orbital. For the sake of simplicity, it maybe represented as shown in figure.

Differences between ORBITS and ORBITALS

Orbits Orbitals

(i) It is well-defined circular patharound the nucleus in which theelectron revolves.

It is a region in three dimensional spacearound the nucleus where the probability offinding electron is maximum

(ii) It is circular in shape s, p and d-orbitals are spherical dumbell anddouble dumbell in shape respectively.

(iii) It represents that an electron movesaround the nucleus in one plane

It represents that an electron can movearound nucleus along three dimensionalspace along x, y and z axis

(iv) The maximum number of electronsin an orbit is 2n2 where n is the

number of the orbit

The maximum number of electrons in anorbital is two

(v) It represents that position as well asmomentum of an electron can beknown simultaneously withcertainty. It is against Heisenbergsuncertainty principle

It represents that position as well asmomentum of an electron cannot be knownsimultaneously with certainty it is inaccordance with Heisenbergs uncertaintyprinciple.

Representation of (a) orbital and (b) orbit.

(a) Orbital (b) Orbit


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29The coordinates x, y, z of electrons w.r.t. nucleus in terms of polar coordinates are given by

x = r sin cos

y = r sin sin

z = r cosAnd solution of schrodinger wave equations gives

nlm = R (r)(n, l), () (l , m) ()(m)

QUANTUM NUMBERS

Quantum numbers are the index numbers, which are used to specify the position and energyof an electron in an atom. The word quantum is used to signify that all the energy levels,which are available to an electron are governed by the laws of quantum mechanics.

There are four quantum numbers. Each of these can have only specific values, which are

inter-related. The values assigned to these numbers determine specific energies that anelectron can have. Each quantum number refers to a particular character of the electron. Inorder to specify completely the position and energy of an electron in an atom, it is necessaryto state the values of each of the four quantum numbers. Just as a person is identified by hisaddress, an electron in an atom is completely known by specifying four quantum numbers.Thus, quantum numbers are complete address of the electrons.

The significant aspects of the four quantum numbers are described below :

1. Principal Quantum Number (n). This quantum number is designated as n and givesthe number of major energy level (shell or orbit) to which the electron belongs. It canhave any positive whole number value excluding zero i.e., n = 1, 2, 3, 4 ...

Thus n can have infinite value and it has been called principal quantum number by Bohr.

Information given by n valuesThe value of n represents the shells which are designated by capital letters K, L M, NThus,

Value of n 1 2 3 4

Letter designationof shells

K

(First shell)

L

(Second shell)

M

(Third shell)

N

(Fourth shell)

(i) The principal quantum number also helps to determine the average distance of theelectron from the nucleus. In terms of quantum mechanics, it gives the effective

volume of the electron cloud.In case of hydrogen atom, the approximate distance from the nucleus is given

by22

22

nme4

hnr

= .


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30Lower value of n represents that the electron is nearer to the nucleus. Thus, nrepresents the size of the electron orbits. Higher is the value of n, larger is the size ofthe electron orbit of atom.

(ii) n also determines the energy of the electron in an orbit. For hydrogen like particles,

it is given by :

22

242

nhn

zme2E

=

Where z is the atomic number, m and e are the mass and charge of the electronrespectively, h is the Plancks constant and n is the number of the orbit.

Substituting the value of m, e, z, n and h, we get

== molkcal

n

6.313molkJ

n

1312E

22n[Q 1 kcal = 4.184 kJ]

The above relation shows that largest negative value of energy 1312 kJ mol1 (i.e.maximum stability) is obtained when n = 1. Thus n = 1 gives the lowest energy state(E1) of an electron in H-atom. This state is called the ground state orstationarystate of an electron in atom.

From above, it is clear that +1312 kJ mol1 energy (called ionisation energy) isneeded to knock out an electron from H-atom.

for n = 2, 11 molkJ328molkJ4

1312E =

=

This reduced negative value indicates that the atom is less stable as compared to the

ground state. Similarly, all states with higher value of n are also less stable. Allstates with n values greater than one are called excited states. When energy calledexcitation energy (which is equal to the energy difference between two states) isprovided, an electron makes a transition from the ground state to one of the excitedstates.

The difference (E) in energy between the two states is given by E =1n2n

EE or a

transition from ground state (n1 = 1) to the first excited state (n2 = 2).

E = E2 E1 = ( 328 kJ mol1) (1312 kJ mol1) = 984 kJ mol1

The various energy states in an atom are commonly called its energy levels.

With the increase in the value n, energy associated with an electron increases andthe energy difference between two successive energy states goes on decreasing.When n becomes infinity, energy becomes zero.

(iii) n value can also be used to calculate the maximum number of electrons that a shellcan hold. Maximum number of electrons in an orbit with principal quantum number ncan have 2n2 electrons.


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31Thus :

The maximum number of electrons in K-shell (n = 1) = 2 12 = 2The maximum number of electrons in L-shell (n = 2) = 2 22 = 8The maximum number of electrons in M-shell (n = 3) = 2 32 = 18

The maximum number of electrons in N-shell (n = 4) = 2 42 = 32.2. Azimuthal, subsidiary, orbital or angular quantum number (l). This quantum number

is given by sommerfield. When hydrogen spectrum was observed by means of aspectroscope of high resolving power, the individual spectral lines were found to consistof a group of closely spaced lines. Such a spectrum consisting of closely spaced spectrallines is called fine structure. The fine structure of a spectral line is explained byassuming that all electrons of a shell do not have same energy and each shell iscomposed of a number of subshells which are specified by a secondary quantumnumber, designated as l.

The value of l depends on the value of n. For a given value of n, l can have values

from zero to (n 1) where n is the value of the principal quantum number.

Information given by l values(i) This quantum number determines the angular momentum of the electron. The

angular momentum is given by the relation :

Angular momentum (mvr) = + 2/h)1(ll or hll )1( +

(ii) The values ofl for a given value of n determine the number of subshells in a shell.For example, when n = 1, the largest (and only) value ofl is zero. Therefore, K-shell

consists of only one subshell. When n = 2, l = 0 and 1. Hence, L-shell is made up oftwo subshells. For n = 3, l = 0, 1, 2, therefore, M-shell consists of three subshells.

(iii) Different values of l represent different subshells which are designated by smallletters s, p, d, f..

For example,

Value of l 0 1 2 3 4 5Designation of sub-shell s p d f g H

For the same value of n, the energies of sub-levels are determined by the value of l

forthem. A sub-level with a higher value of l is associated with higher energy. Thus,

s < p < d < f (for same value of n)

(l = 0) (l = 1) (l = 2) (l = 3)

(iv) The shape of an orbital is also related to its l value. When l = 0, the orbital isspherically symmetrical and is known as s-orbital. When l = 1, the orbital is dumbell


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32shaped and is called p-orbital. Similarly, orbitals having l = 2 and 3 are known as dand f-orbitals respectively. The d-orbitals are double dumbell shaped whereas the f-orbitals have more complex shape.

The letters s, p, d and f find origin in the atomic spectra of the alkali metals. In thesespectra, four series of lines were observed and were termed the sharp, principal,diffuse and fundamental series, hence the letters s, p, d and f.

To specify a subshell within a given shell, we write the value of n for the shell followedby the letter designation of the subshell. For example, s-subshell of the first shell(n = 1, l = 0) is known as 1s-subshell. Similarly, the p-subshell of the second shell(n = 2, l = 1) is known as 2p-subshell. The designations of subshells for n = 1 to n = 5are given below.

n l subshell designation No. of subshells in a shell1 0 1s One

2 01

p2s2 Two

3 0

1

2

d3

p3

s3

Three

4 0

1

2

3

f4

d4

p4

s4

Four

5 0

1

2

3

4

g5

f5

d5

p5

s5

Five

(v) l-values also enable us to calculate the total number of electrons in a given subshell(s, p, d and f subshell). The total number of electrons in a given sub-shell with a givenl value is equal to 2(2l + 1). For example,

Value of l 0 1 2 3 4 5sub-shells s p d f g h

No. of electrons in a sub-

shell = 2(2l + 1) = 4l + 22 6 10 14 18 22


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333. Magnetic quantum number (m or ml). It has been observed that a moving electron in a

subshell is associated with a magnetic field. When an atom is placed in an externalmagnetic field, the orbitals of same kind (e.g. px, py and pz orbitals) are no longer identicalin energy because some of them are parallel to the magnetic field while others are not.

As a result, electrons get excited from one of these orbitals to another and give additionallines. In other words, the finer lines of spectrum further split up. This phenomenon wasfirst of all studied by Zeeman and is called Zeeman effect. In order to correlate theseenergy changes, magnetic quantum number (m or m

l) was suggested.

Under the influence of external magnetic field, electrons in a sub-shell adjust themselvesin different orientations. The orientations (or preferred regions in space) are calledorbitals. Thus each sub-shell is composed of orbitals. Each orbital is designated by adifferent value of m.

The values of m range from l to zero to + l and maximum values of m = 2l + 1. Forexample

When l = 0 (s-subshell), m = 0 (Only one value)

When l = 1 (p-subshell), m = 1, 0, +1 (Three values)

When l = 2 (d-subshell), m = 2, 1, 0, +1, +2 (Five values)

When l = 3 (f-subshell), m = 3, 2, 1, 0, 1, 2, 3 (Seven values)

Information gives by m values. m values for a given value ofl are used to calculate thenumber of orbitals in a sub-shell. For a given value ofl, the number of m values is equalto the number of orbitals in a subshell. In terms of l values, the number of orbitals in asub-shell is equal to 2l + 1. For example,

(i) When n = 1, l = 0 (s-subshell), m = 0 (l to 0 to +l), i.e. only one value of m ispermitted. Hence, s-subshell is composed of only one orbital.

(ii) When n = 2, l = 0, 1. When l = 0, m = 0 but when l = 1, m = 1, 0, +1. Therefore, forl = 1, (p-subshell), there are three permitted values of m. Hence, p-subshell iscomposed of three orbitals known as px, py and pz orbitals.

(iii) When n = 3, l = 0, 1, 2. Forl = 2 (d-subshell) m = 2, 1, 0, +1, +2. Thus, d-subshellis composed of five different orbitals.

(iv) When n = 4, l = 0, 1, 2, 3. Forl = 3 (f-subshell) m = 3, 2, 1, 0, +1, +2 and +3. fore,f-subshell is composed of seven orbitals.

Maximum number of orbitals in a shell = n2. For example, maximum number of orbitals in:(i) first shell = 12 = 1 (1s)

(ii) second shell = 22 = 4 (2s, 2px, 2py, 2pz)

(iii) third shell = 32 = 9 (3s, 3px, 3py, 3pz,3dxy, 3dyz,

3dzx , 2y2xd3

, 3dz

2


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34

The number of subshells and orbitals in thefirst three shells (K, L, M) are shown in Fig.

4. Spin Quantum Number (s). This quantum number is given by Gold Schmidth.In 1921, theGerman physicists Otto Stern and Walter Gerlach passed a beam of neutral silver atoms(obtained from the vaporisation of silver) between the poles of a specially designed magnet.The beam was found to split into two separate beams (Fig.) i.e. half the atoms weredeflected in one direction, and the rest in the opposite direction. This means that half of the

silver atoms are acting like magnets pointing in one direction and the other half in theopposite direction. To explain this magnetic behaviour, it was assumed that an electron spinsaround its own axis and this spin creates a small magnetic field. Thus, an electron acts like atiny magnet. An electron can spin either clockwise or anticlockwise. Thus, it can have two

possible values2

1+ or

2

1 . These values depend upon the direction of the spin. As a rule,

when two electrons are present in an orbital, these have opposite spins (). By convention

( ) )rotationiseanticlockw(2

1androtationclockwise

2

1+

Shapes of Atomic Orbitals or Boundary Surface Diagrams

The probability of finding the electron does not become zero even at large distances from thenucleus. Therefore, it is not possible to draw any sort of geometrical figure that will enclose aregion of 100% probability.

Radial Wave FunctionsThe shapes of orbitals are obtained from the variation of wave function as a function of r(distance from the nucleus). This is also called radial dependence or radial wave function.This can be shown in a simple method by plotting a graph between wave function ( ) anddistance (r) from the nucleus.

These graphs are shown for 1s, 2s and 2p orbitals in figure. It is clear from figure(a) thatwave function for 1s-orbital continuously decreases with increase in r. However, for 2s-orbital

fig (b), the wave function decreases in the beginning with increase in r.

3d

3p

3s

n = 3 or MShell

3d (five)

3p (three)

3s (one)

2p

2s

n = 2 or LShell

2p (three)

2s (one)n = 1 or K

Shell1s

Subshell1s (one)Orbital

Number of subshells and orbitals in firstthree shells (K, L and M)


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35

This point at which radial wave function becomes zero is called radial nodal surface or simplynode. At the node, the value of wave function changes from positive to negative. In general, ithas been found that ns orbitals have (n 1) nodes. Similarly, np orbitals have (n 2) nodesand so on. In all cases, approaches zero as r approaches infinity.

Probability Density (2) GraphsAccording to the German physicst, Max, Born, the square of the wave function, 2 at a pointgives the probability density of finding the electron at that point. These variations of2 as afunction of r are obtained by plotting 2 against r.These plots for 1s, 2s and 2p orbitals are shown in figure. These graphs are called probabilitydensity graphs. It may be noted that for s-orbitals (1s and 2s), the maximum electron densityis at the nucleus and for p-orbitals (2p), it has zero electron density at the nucleus. It may benoted that all orbitals except s-orbitals have zero electron density at the nucleus.

Radial Probability Functions ( 4r22)In order to determine the total probability in an infinitesimally small region, we have to multiplyprobability density (2) by the volume of region, i.e.

Probability = 2 dVwhere dV is the volume of the region. Since the atoms have spherical symmetry, it is more

useful to discuss the probability of finding the electron in a spherical shell between thespheres of radius (r + dr) and r.This gives the total probability of finding the electron at a particular distance (r). This is calledradial probability. The plots of probability (4r22] as a function of distance from the nucleus(r) are called radial probability distribution function (r.d.f.) graphs.It is clear that the radial probability distribution graphs depend not only upon the probabilitydensity but also on the volume of the shell. The probability density (2) for 2s is maximum

(b)

r

2s Orbital

Node

Distance from thenucleus

1s Orbital

(a)

r

2p orbital

(c)


3s Orbital

Nodes2


2s Orbital

Node2


1s Orbital

2

r

2p orbital

2


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36near the nucleus and it goes on decreasing with distance. However, the volume of the shellgoes on increasing with increase in distance. The product of probability density and volumeof shell gives the radial probability (4r22) and is plotted against the distance from thenucleus.

The graph for 1s-orbital shows that the probability of finding the electron is zero at nucleus, itkeeps on increasing and becomes maximum at a particular distance from the nucleus andthen gradually decreases. This is called the radius of maximum probability.The radial probability functions versus distance r from the nucleus for 1s, 2s and 2p orbitalsare shown in figure.

Shapes of s-orbitalss-orbitals are non-directional and spherically symmetrical. This means that the probability offinding the electron is same in all directions at a particular distance from the nucleus.There is a spherical shell within 2s-orbital where the probability of finding the electron ispractically zero. This is called a node or a nodal surface.

Shapes of p-orbitals : On the basis of probability circulation, it has been found that the

probability of finding the p-electrons is maximum in two lobes on the opposite side of thenucleus, thus giving rise to a dumb-bell shape for the p-orbital. Further, the probability offinding a particular p-electron is equal in both the lobes. There is a plane passing through thenucleus on which the probability of finding the electron is almost zero. This is called a nodalplane.

4r

2dr

2

1s- orbitalr r

2s- orbital

Node

r

4r2dr

2

r

2p- orbital

4r

2dr

2

Nodal Sphere

NodalSphere

1S 2S 3S


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37For p-subshell, l = 1. Hence m = 1, 0, + . Thus p orbitals have three orientations. Theseare designed as px, py and pz depending upon whether the electron density is maximumalong the X axis, Y axis and Z axis respectively.There is no probability of finding a p-electron right at the nucleus. Directional nature of p-orbitals

help us in predicting the shapes of the molecules

Shapes of d OrbitalsThere are five degenerate d-orbitals corresponding to l =2 in each d subshell corresponding tom = 2, 1, 0, +1, +2. These are double dumb bell shaped four of these 5 orbitals have the sameshape but differ in orientation in space. They have four lobes of electron density and two nodalplanes. One of these four lobed d orbitals, has maximum density along X and Y axes. It iscalled .d 2y2x For the other three, the directions along which the electron density is maximum lie

at 45o to the coordinate axis. These are dxy, dyz and dxz orbitals.The fifth d orbital ( 2zd ) has two lobes of electron density directed along the Z axis and a

ring of electron density (called a doughnut) centred in XY plane. The shape of this orbital( 2zd ) quite similar to baby soother. dxy, dxz and dyz orbitals having their greatest electron

densities in the region between the axes are called t2g or d. The other two namely 2zd and2y2x

d

have their greatest electron densities in the directions that lie along the axes and also

known as eg or dy.

Shapes of f-orbitals

There are seven degenerate orbitals with l = 3 and m = 3, 2, 1, 0, +1, +2, +3 in each subshells. These orbitals are complicated in shape. They possess 8 lobes with threenodal planes.

+

X

PX

z

yyz Nodal Plane

+X

PX

z

y

xzNodal Plane

+

X

Pz

z

y

Nodal Plane

Y

dxy

Z

X Y

dyz

Z

X

dxz

t2g or de

Z

X

dx2

y2

Z

X

dz2

eg or dr


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38

Nodes and Nodal planesAs we have learnt nodes are the positions where radial wave function passes through zero.These are also called radial nodes.

Beside radial nodes, the probability density functions for np and nd orbitals are zero at theplanes passing through the nucleus. For example as shown in figure, in case of 2p3 orbital, xyplane is a nodal plane. This is called Angular Node or Nodal Plane. Similarly, for of the 3dorbitals (3dxy, 3dyz, 3d3x and 2y2x

d3

) have two perpendicular nodal planes that intersect in a

line passing through the nucleus. For example, 3dxy orbital have two nodal planes, passingthrough the origin and bisecting the xy plane containing z-axis. The number of angular nodesor given by l i.e, one angular node for p orbitals, two angular nodes for d-orbitals and so on.In general, in an orbital :Total number of nodes = n 1Angular nodes = l

Radial nodes = n l 1.Paulis Exclusion Principle

Wolfgang Pauli (1925) studied atomic spectra of elements and discovered the principle calledPaulis exclusion principle. According to this principle, No two electrons in an atom can haveall the four quantum numbers alike.

Applications

1. An orbital cannot have more than two electrons. Consider three electrons e1, e2, e3(having spin values s as shown against each) present in one orbital.

Electrons e1 e2 e3

Values of s21+

21

21+ or

21

(i) Two electrons, e1, e2 of the same orbital will have same values of n, l and m. Spin

value can be either2

1+ or

2

1 so that exclusion principle is obeyed.

(ii) For the electron, e3, let value of s =2

1+ . In this case, the value of four quantum

numbers for e1 and e3 will be same

(iii) For the electrons e3, let value of s =2

1 . In this case, the value of four quantum

numbers for e2 and e3 will be same. The (ii) and (iii) possibilities are denied by Pauliexclusion principle. Hence an orbital can not accommodate more than two electrons.

2. Maximum number of electrons in a sub-shell. Paulis exclusion principle can be used tocalculate the number of electrons in different subshells. For s-subshell (l = 0), m = 0 i.e. s-subshell has only one orbital and hence can accommodate only two electrons. For p-subshell(l = 1), m = 1, 0 and 1 i.e. a p-subshell has three orbitals, so that it can have 2 3 or six


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39electrons. For d-subshell (l = 2), m = 2, 1, 0, 1, 2 i.e. a d-subshell has five orbitals andhence 5 2 or 10 electrons. For f-subshell (l = 3), m = 3, 2, 1, 0, 1, 2, and 3 i.e. a f-subshell can have seven orbitals and hence 2 7 or 14 electrons.

3. Maximum number of electrons in a shell. The number of orbitals in a shell = n2.Therefore, maximum number of electrons in an orbit = 2n2. Thus, maximum number ofelectrons in first shell = 2 12 = 2. Maximum number of electrons in second shell = 2 22= 8 and so on. The maximum number f electrons in different sub levels and shells areshown in table.

Subdivisions of main energy levels

Main energy level (n) 1 2 3 4 5Number of sublevels (n) 1 2 3 4 5Type of sublevels s s, p s, p, d s, p, d, f s, p, d, f, gNumber of orbitals per sublevel 1 1,3 1, 3, 5 1, 3, 5, 7 1, 3, 5, 7, 9

Maximum number of electrons persublevel (4l + 2) 2 2, 6 2, 6, 10 2, 6, 10, 14 2, 6,10,14,18

Maximum number of electrons permain level (2n2)

2 8 18 32 50

Electronic Configuration of Elements

The electrons are distributed among the orbitals of an atom is the electronic structure orelectronic configuration. The electronic configuration of the elements are constructed byassuming that the electrons occupy the lowest possible energy leve

001 a a strucure syn

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