Chem 1A03

Chapter 8: Electrons in Atoms 8.1 Electromagnetic Radiation Electromagnetic Radiation: A form of energy transmission in which electric and magnetic fields are

propagated as waves through empty space (a vacuum) or through a medium (such as glass) Wave: A disturbance that transmits energy through space or a material medium

o Crests – high points o Troughs – low points o Amplitude – maximum distance from the center line, above or below o Wavelength – λ lambda; the distance between two successive crests (or the bottoms of two troughs)

SI unit: m (meter) o Frequency – ν nu; the number of crests or troughs that pass through a given point per unit of time

Time-1, or s-1 (per second) SI unit: Hz (Hertz)

o Speed of Wave – C; product of λ and ν C = λ x ν

Magnetic field component lies in a plane perpendicular to the electric field component o Figure 8-2, page 296; o Electric Field – the region around an electrically charged particle; presence can be detected by

measuring the force on an electrically charged object when it is brought into the field o Magnetic field – found in the region surrounding a magnet

Theory – James Clerk Maxwell in 1865 o Electromagnetic radiation is produced by an accelerating electrically charged particle o Eg/ Radio waves – are a form of electromagnetic radiation produced by causing oscillations

(fluctuations) of the electric current in a specially designed electrical circuit o Eg/ Visible light – the accelerating charged particles are the electrons in atoms or molecules

Speed of light – electromagnetic radiation has a constant speed in a vacuum; 2.99792458 x 108 m s-1

An Important Characteristic of Electromagnetic Waves Constructive Interference – the addition of waves In Phase – where two waves crests, or two waves troughs coincide and create the highest crest or lowest

trough Out of Phase – where one waves crest and one waves trough coincide and the waves cancel each other out

causing the wave to be flat Destructive Interference – the cancelation of waves Diffraction – the dispersion of different wavelength components of a light beam through the interference

produced by reflection from a grooved surface

Chem 1A03 The Visible Spectrum Refraction – the bending of light; occurs when it passed from one medium to another

Suns Emission Spectrum

Earth’s Protective Shield Ozone Ozone and UV Exposure

o Approximately 90% UVB radiation (280-320 nm) from the sun is selectively absorbed by photolysis of O3 in the stratosphere, with peak at approx. 20km from Earths surface

o Lover O3 levels increase the transmittance of UVB radiation to earth – Montreal Protocol: 1987

Biological Impacts

o UV B radiation can ionize biological molecules (DNA, Protein) o Chronic exposure to UVB rays increases chance of skin cancer,

cataracts and genetic mutations o Body’s response: Produce melanin (dark pigment) to filter UVB

radiation Tan is melanin; it absorbs light, prevents UV from entering the bodies biological molecules

Chemistry of Sunscreen

o Propose alternative ways to decrease exposure to UC radiation

o Use of sunscreen/cosmetics containing UV absorbing chemicals

8.2 Atomic Spectra Discontinuous Spectrum – is observed if the source of a spectrum

produces light having only a relatively small number of wavelength components

Atomic Spectra - The emitted light produces a spectrum consisting of only a limited number of discrete wavelength components, observed as colored lines with dark spaces between them

o Eg/ If the light source is an electric discharge passing through a gas, only certain colors are seen in the spectrum

Figure 8-8a,b, page 300 o Eg/ If the light source is a gas flame into which an ionic compound has been introduced, the flame may

acquire a distinctive color indicative of the metal ion present Figure 8-8c-e, page 300

Production of the line spectrum o Figure 8-9, page 301 o Light source is a lamp containing helium gas at a low pressure

Chem 1A03 o When an electric discharge is passed through the lamp, the elements atoms absorb energy, which then

emit as light o The light is passed through a narrow slit and them dispersed by a prism o The colored components of the light are detected and recorded on photographic film o Each wavelength appears as a thin line

Robert Bunsen and Gustav Kirchhoff developed the first spectroscope and used it to identify elements Johann Balmer deduced a formula for the wavelengths of spectral lines

o ν = 3.2881 x 1015 s-1 (1/22 – 1/n2) o ν = the frequency of the spectral line o n must be an integer greater than 2

The fact that the atomic spectra consists of only limited numbers of well-defined wavelength lines provides a great opportunity to learn about the structures of atoms

o Suggests that only a limited number of energy values are available to excited gaseous atoms

8.3 Quantum Theory Blackbody radiation – light emission from heated solids Classical theory – predicts that the intensity of the radiation emitted would increase indefinitely

o Figure 8-11,page 302 o No limitation on the amount of energy as system may possess

Quantum Theory – energy, like matter, is discontinuous o Proposed by Max Planck o Limits energy to a discrete set of specific values o Quantum of energy – the difference between any two allowed energies of a system

Model used for the emission of electromagnetic radiation – a group of atoms on the surface of the heated object oscillating together with the same frequency

o ε = nhν where ε = Energy n is a positive integer ν = oscillator (group of atoms) frequency h = 6.62607x10-31 J s (Planck’s constant)

The energy of a quantum of electromagnetic radiation is proportional to the frequency of the radiation o Planck’s Equation: E = hν

The Photoelectric Effect Heinrich Hertz, 1888, discovered that when light strikes the surface of certain metals, electrons are ejected Electron emission only occurs when the frequency of the incident light exceeds a particular threshold value (ν0)

o The number of electrons emitted depends on the intensity of the incident light o The kinetic energies of the emitted electrons depend on the frequency of the light

Einstein, 1905, proposed that electromagnetic radiation has particle-like qualities, these particles of light called photons, have a characteristic energy give by Planck’s equation

Particle Model o A photon of energy hν strikes a bound electron, which absorbs the photon energy

Chem 1A03 o If the photon energy, hν, is greater than the energy binding the electron to the surface (quantity known

as work function), a photoelectron is liberated (Ephoton > Threshold Energy of metal e- is ejected with kinetic energy)

o Thus – the lowest frequency light producing the photoelectric effect is the threshold frequency, and any energy in excess of the work function appears as kinetic energy in the emitted photoelectrons

Key Observations o Work function (threshold energy, hν0) of the metal must be

overcome for e- to be emitted o When incident light frequency exceed a threshold value (ν0) e- are

emitted o # of electrons (current) emitted depends on light intensity (# of

photons) o Kinetic Energy of emitted electrons depends on Energy of light o E (incident light) = Threshold E + KE of e-

Figure 8-12a, page 304; The Photoelectric Effect o First circuit

Light (hν) is allowed to shine on a piece of metal in an evacuated chamber The electrons emitted by the metal (photoelectrons) travel to the upper plate and complete an

electric circuit set up to measure the photoelectric current through an ammeter

Figure 8-12b, page 304; The Photoelectric Effect o First circuit

Illustrates the variation of the photoelectric current, Ip, through an ammeter as the frequency (ν), and the intensity of the incident light is increased

No matter how intense the light, no current flows if the frequency is below the threshold frequency, ν0, and no photoelectric current is produced

No matter how weak the light, there is a photoelectric current if ν > ν0 The magnitude of the photoelectric current is directly proportional to the intensity of the light,

so that the number of photoelectrons increases with the intensity of the incident light We can associate light intensity with the number of photons arriving at a point per unit time

Figure 8-12a, page 204; The Photoelectric Effect o Second circuit

Measures the velocity of the photoelectrons A potential difference (voltage) is maintained between the photoelectric metal and an open-grid

electrode placed below the upper plate For electric current to flow, electrons must pass through the openings in the grid and onto the

upper plate The negative potential on the grid acts to slow down the approaching electrons As the potential difference between the grid and the emitting metal is increased, a point is

reached at which the photoelectrons are stopped at the rid and the current ceases to flow through the ammeter

At the stopping voltage (the potential difference when the current ceases to flow), the kinetic energy of the photoelectrons has been converted to potential energy, expressed through the following equation

½ mu2 = eVs

m = mass of electron u = speed of electron e = charge of electron

Vs is proportional to the frequency of the incident light, but independent of the light intensity, is below the threshold frequency, ν0, no photoelectric current is produced

At frequencies greater than ν0, the empirical question for the stopping voltage is Vs = k(ν – ν0) Constant k is independent of the metals used

Chem 1A03 ν0 varies from one metal to another

There is no relation between Vs and light intensity – but photoelectric current, Ip, is proportional to the intensity of light

o The work function is a quantity of work and of energy o One way to express this quantity is as the product of Planck’s constant and the threshold

frequency E = hν o Another way is as the product of the charge on the electron, e, and the potential, V0, that has

been overcome in the metal: E = eV0 o Thus, the threshold frequency for the photoelectric effect is given by:

ν0 = eV0 h

o Since the work function (eV0) is a characteristic of the metal used in the experiment, the ν0 is also characteristic of the metal

o When a photon of energy hν strikes an electron, the electron overcomes the work function eV0 and is liberated with kinetic energy (1/2 mu2) We have ½ mu2 + eV0 – hν Which gives eVs = ½ mu2 = hν – eV0

Which is identical to the empirically determined equation for Vs with k = h/e when hν0

Photons of Light and Chemical Reactions Photochemical reactions – chemical reactions that are induced by light

o Photons – like reactants, designate symbol hν o Eg/ Ozone

O2 + hν O + O O2 + O + M O3 + M* First reaction – UV radiation with wavelength less than 22.4 nm; O atoms combine with O2 to form O3 Second reaction – a “third body”, M, is needed to carry away excess energy to prevent immediate dissociation of O3 molecules

8.4 The Bohr Atom Bohr postulated that for a hydrogen atom:

1. The electron moves in circular orbits about the nucleus with the motion described by classical physics 2. The electron has only a fixed set of allowed orbits, called stationary states

o The allowed orbits are those in which certain properties of the electron have unique values o As long as an electron remains in a given orbit, its energy is constant and no energy is emitted o Angular Momentum – the particular property of the electron having only certain allowed values,

leading to only a discrete set of allowed orbits o It’s possible values are nh/2π, where n must be an integer o Thus the quantum numbers progress: n = 1 for the first orbit, n=2 for the second etc

3. An electron can pass only from one allowed orbit to another. In such transitions, fixed discrete quantities of energy (quanta) are involved – either absorbed or emitted

Figure 8-13, page 308; Bohr Model of Hydrogen Atom Quantum numbers – the integral numbers which arose from Bohr’s assumptions that only certain value are

allowed for the angular momentum of the electron; n=1,2,3,4 Bohr Theory predicts the radii of the allowed orbits in a hydrogen atom

rn = n2A0 Where n = 1,2,3… a0 = 52 pm

The theory also allows us to calculate the electron velocities in these orbits an the energy o When the electron is free of the nucleus it is said to be at a zero of energy o When a free electron is attracted to the nucleus and confined to the orbit, n, the electron energy

becomes negligible, with its value lowered to En = - RH

n2

Chem 1A03 RH = 2.179 x 10-18 J

We can use this expression to calculate the energies of the allowed energy states, or energy levels of the hydrogen atom

Can be represented in an energy-level diagram (Figure 8-14, page 309) Can predict whether energy levels are possible or impossible

Ground State – lowest allowed energy

o n = 1 Excited State – when an electron gains a quantum of energy, it moves to a higher level

o n > 1 Ionized

o n = ∞ When an electron drops from a higher level to a lowered numbered orbit, a quantity of energy is emitted (the

difference in energy between the two levels) ΔE = Ef – Ei = -RH – -RH n2f n2i = RH ( 1 – 1 ) n2i n2f

= 2.179 x 10-18 J( 1 – 1 )

n2f n2i

May be positive (absorption) or negative (emission) The energy of the photon, Ephoton, either absorbed or emitted, is equal to the magnitude of this energy difference

Ephoton = hν = |ΔE|

Einstein’s Proposal Light is quantized like a particle (photons)

Ephoton = hν and Ephoton = ΔE ΔE atom = hν = threshold energy + ½mu2

E = hν = hc/λ =threshold energy + ½mu2

Where ½mu2 = speed of any moving object The Bohr Theory and Spectroscopy Emission Spectra are obtained when the individual atoms in a collection of atoms are excited to the various

possible excited states of the atom – the atoms then relax to states of lower energy by emitting photons of frequency

νphoton = Ei - Ef h Thus, the quantization of the energy states of atoms leads to line spectra

Chem 1A03 Spectroscopy

o Absorption Spectroscopy – pass electromagnetic radiation (eg/ white light) through a sample of atoms in their ground states and then pass the emerging light through a prism

Observe which frequencies of light the atoms absorb νphoton = Ef - Ei

h o Figure 8-15, page 311 o The farther apart the energy levels, the shorter

the wavelength of the photon needed to induce a transition

Atomic Absorption – Lead Analysis Pb in Water, Food, Fuels, Paint and Toys Lead is a toxic element notably for infants

neurological development Selective analysis of Pb via flame atomic absorption

spectroscopy o AAS detects atomized metal ions from

aqueous solution o Lead cathode lamp excited sample

(absorption) through flame, and an emission spectrum is produced

o Decrease in intensity of light _217 nm) through flame related to conc. of Pb

The Bohr Theory and the Ionization Energy of Hydrogen In special cases, where the energy of a photon interacting with a hydrogen atom is just enough to remove an

electron from the ground state (n=1), the electron is fixed, the atom is ionized and the energy of the free electron is zero

hνphoton = Ei = -Ef

o The quantity Ei is called the ionization energy of the hydrogen atom o If ni = 1 and nf = ∞ are substituted into the Bohr expression for an electron initially in the ground state

of an H atom hνphoton = Ei = -Ef = RH = RH

12

The nuclear charge (atomic number) appears in the energy-level expression, for species such as ions He+ and Li2+ (have only one electron) En= -Z2RH n2

H atom ionization: Electron absorbs enough enerhy to escape the atom H H+ + e-

e- moves from its initial n state (ni) to a final n state (nf), where nf = ∞ ΔE = Ef – Ei

But EF = - RH = -1 = 0

n2f X2

The energy it takes to free the electron is ΔE = -E

Flame Atomic Absorption: Set-Up

Chem 1A03

Inadequacies of the Bohr Model The theory cannot explain the emission spectra of atoms and ions with more than one electron The theory cannot explain the effect of magnetic fields on emission spectra The theory is an uneasy mixture of classical and non-classical physics

8.5 Two Ideas Leading to a New Quantum Mechanics Wave-Particle Duality: Theory Louis de Broglie: particles (e-) display wave properties

o From E = mc2 (Einstein) and E = hν (Planck) and vλ=c λ = h/mu λ = h/ρ

Particles should display wave properties o Eg/ diffraction o If distance between objects that the waves scatter is the same as the radiation λ, diffraction occurs

Thomason’s Electron Diffraction Experiment (Nobel Prize) Radiation and object spacing are similar: X-rays, λ = 100pm Metal foil, regular array of metal atoms, 200 pm spacing 8.6 Wave Mechanics Schrodinger equation: Combines ideas of particle and wave

behavior to describe the sat of e- in atom Orbitals

o Are wave functions, Ψ, solutions to the Schrodinger equation o Orbitals are described by 3 quantum numbers o Orbitals describe regions of high probability of finding an electron (high charge density)

8.7 Quantum Numbers and Electron Orbital’s Assigning Quantum Numbers Principal Quantum Number, n

o n = 1,2,3,4… o n relates to the energy and most probably distance of an electron from the nucleus – higher value,

greater electron energy and farther away Orbital Angular Momentum Quantum Number, l

o l = 0,1,2,3… n – 1 o Cannot be larger than n-1 o l determines the angular distribution, or shape, of an orbital o l = 0 s subshell o l = 1 p subshell o l = 2 d subshell o l = 3 f subshell

Magnetic Quantum Number, ml o ml = -1, (-l + 1), …, -2, -1, 0, 1, 2 …, (l – 1), +l o Ranges from -l to +l o ml determines the orientation of the orbital

Principle Shells and Subshells All orbitals with the same value n are in the same Principle Electronic Shell or Principal Level All orbitals with he same n and l value are in the same Subshell or Sublevel The number of subshells in a principal electronic shell is the same as the principal quantum number

Chem 1A03 o Eg/ n=3 3 subshells (l = 0,1,2)

The number of orbitals in a subshell is the same as the number of allowed values for ml for the particular value of l

o Eg/ l = 1 ml = -1,0,+1 the number of orbitals = 3 o 2l + 1

The energies of the orbitals for a hydrogen atom, in joules, are given by o En = -2.178 x 10-18 (1/n2) J o All subshells within a principal electronic shell have the same energy o All orbitals within a subshell have the same energy

Orbitals at the same energy level are said to be degenerate

8.8 Interpreting and Representing the Orbitals of the Hydrogen Atom Orbital Pictures

o S orbitals are spherical 1s, 2s, 3s at 95% probability

o P orbitals (px, py, pz) I angular node )0 probablity of finding electron) Possible in n ≥ 2

o D orbitals (cross section) 2 angular nodes Possible in n ≥ 3

8.9 Electron Spin: A Fourth Quantum Number Electrons Spin Quantum Number, ms

o + ½ (), - ½ () o Does not depend on any other quantum number o Pair of e- with opposite spins has no magnetic field o Atoms or ions with all spins paired are diamagnetic o Atoms or ions with 1 or more unpaired electrons are paramagnetic

Proof – Otto Stern and Walter Gerlach o Silver was vaporized in an over and a beam of silver atoms was passed through a nonuniform magnetic

field, where the beam split in two An electron, because of its spin, generates a magnetic field A pair of electrons with opposing spins has no net magnetic field In the silver atom, 23 electrons have a spin of one type and 24 of the opposite type. The

direction of the net magnetic field produced depends only on the spin of the unpaired electron Ina beam of a large number of silver atoms there is an equal chance that the unpaired electron

will have a spin of + ½ or – ½ . the magnetic field induced by the silver atoms interacts with the nonuniform field, and the beam of silver atoms spits into two beams

o Figure 8-33, page 334

8.10 Multielectron Atoms 8.11 Electron Configurations The electron configuration of an atom is an designation of how electrons are distributed among various

orbitals in principal shells and subshells Electron Configuration of an atom is a designation of how electrons are distributed among various orbitals in

principal shells and subshells Rules for Assigning Electrons to Orbitals

1. Electrons occupy orbitals in a way that minimizes the energy of the atom 2. Pauli Exclusion Principle – No two electrons in an atom can have all four quantum numbers alike

Only two electrons may occupy the same orbital, and these electrons must have opposing spins 3. Hund’s Rule – When orbitals of identical energy (degenerate orbitals) are available, electrons initially

occupy orbitals singly

Chem 1A03 Representing Electron Configurations Condensed spdf notation Expanded spdf notation Orbital Diagram Energy-Level Diagram Electron Configuration Noble-Gas-Core-Abbreviated Electron Configuration Ground State – parallel spins Excited State – opposite spins The Auf Bau Process Auf Bau – “building up” Assign electron configurations to the elements in order of increasing atomic number

8.12 Electron Configurations and the Periodic Table