chapter 6 electronic structure of atoms

ElectronicStructureof Atoms

Chapter 6Electronic Structure

of Atoms

Chemistry, The Central Science, 10th editionTheodore L. Brown; H. Eugene LeMay, Jr.; and Bruce E. Bursten

John D. BookstaverSt. Charles Community College

St. Peters, MO 2006, Prentice Hall, Inc.


October 31Next test unit 6 and 7 together

• The nature of waves • 6.9 to and 6.17 ODD 6.12• Photoelectric Effect• Line Spectra• Bohr Model• Quantum Model• Hw for the whole chapter 6• 21to 37 odd only and 43• 47 to 53 odd only• 63,66,67,68,71,72,73,75


Waves

• To understand the electronic structure of atoms, one must understand the nature of electromagnetic radiation.

• The distance between corresponding points on adjacent waves is the wavelength ().


Waves• The number of waves

passing a given point per unit of time is the frequency ().

• For waves traveling at the same velocity, the longer the wavelength, the smaller the frequency.


Waves

• Long Wavelength• Low Frequency• Low energy

• Short Wavelength• High Frequency• High energy


Light and Waves• All waves have a characteristic wavelength, (lambda)

and amplitude, A.• The frequency, (nu) of a wave is the number of cycles

which pass a point in one second.• The speed of a wave, v, is given by its frequency

multiplied by its wavelength:

• For light, speed = c.

cm∙s-1 Hz (s-1) m


Electromagnetic Radiation

• All electromagnetic radiation travels at the same velocity: the speed of light (c)

3.00 108 m/s.• Therefore,

c =


• Modern atomic theory arose out of studies of the interaction of radiation (light) with matter.

• Electromagnetic radiation moves through a vacuum with a speed of 2.99792458 108 m/s.

• Electromagnetic waves have characteristic wavelengths and frequencies.

• Example: visible radiation has wavelengths between 400 nm (violet) and 750 nm (red).


The Wave Nature of LightThe Wave Nature of Light


Examples

1. Calculate the frequency of light with a wavelength of 585 nm.

2. Calculate the wavelength of light with a frequency of 1.89 x 1018 Hz.


The Nature of Energy• The wave nature of light

does not explain how an object can glow when its temperature increases.

• Max Planck explained it by assuming that energy comes in packets called quanta.


NOVEMBER 1

• Plank – proposed quantization of energy• Einstein – proposed and explanation for the

photoelectric effect. Light behave like a particle- Photon-

• BOHR THEORY AND THE SPECTRA OF EXCITED ATOMS

• BALMER SERIES AND LYMAN SERIES


• Planck: energy can only be absorbed or released from atoms in certain amounts called quanta.

• The relationship between energy and frequency is

where h is Planck’s constant (6.626 10-34 J·s).• To understand quantization consider walking up a ramp

versus walking up stairs:• For the ramp, there is a continuous change in height whereas up

stairs there is a quantized change in height.

Quantized Energy and Quantized Energy and PhotonsPhotons

hE


The Nature of Energy

• If one knows the wavelength of light, one can calculate the energy in one photon, or packet, of that light:

c = E = h


The Photoelectric Effect and Photons• The photoelectric effect provides evidence for the particle

nature of light -- “quantization”.• If light shines on the surface of a metal, there is a point at

which electrons are ejected from the metal.• The electrons will only be ejected once the threshold

frequency is reached (work function- energy needed for an electron to overcame the attractive forces that hold it in a metal.

• Below the threshold frequency, no electrons are ejected.• Above the threshold frequency, the number of electrons

ejected depend on the intensity of the light.



• Einstein used this assumption to explain the photoelectric effect.

• He concluded that energy is proportional to frequency:

E = hwhere h is Planck’s constant, 6.63 10−34 J-s.


• Einstein assumed that light traveled in energy packets called photons.

• The energy of one photon:hE


Einstein

• Said electromagnetic radiation is quantized in particles called photons.

• Each photon has energy = h = hc/

• Combine this with E = mc2

• You get the apparent mass of a photon.

• m = h / (c)


Examples

1. Calculate the energy of a photon of light with a frequency of 7.30 x 1015 Hz.

2. Calculate the energy of red light with a wavelength of 720 nm.

3. Calculate the energy of a mole of photons of that red light.

4. Calculate the wavelength of a photon with an energy value of 4.93 x 10-19 J.


Examples

1. Calculate the energy of a photon of light with a frequency of 7.30 x 1015 Hz.

4.84 x 10-18 J

2. Calculate the energy of red light with a wavelength of 720 nm.

2.76 x 10-19 J

3. Calculate the wavelength of a photon with an energy value of 4.93 x 10-19 J.

403 nm (4.03 x 10-7 m)



Another mystery involved the emission spectra observed from energy emitted by atoms and molecules.

When gases at low pressure were placed in a tube and were subjected to high voltage, light of different colors appeared


Continuous Spectra• Radiation composed of only one wavelength is called

monochromatic.• Radiation that spans a whole array of different

wavelengths is called continuous.• White light can be separated into a continuous spectrum

of colors.• Note that there are no dark spots on the continuous

spectrum that would correspond to different lines.

Line Spectra and the Bohr Line Spectra and the Bohr ModelModel


Line Spectra

If high voltage is applied to atoms in gas phase at low pressure light is emitted from the gas.

If the light is analyzed the spectrum obtained is not continuous.

SPECTROSCOPE


Line Spectra.

When the light from a discharge tube is analyzed only some bright lines appeared.


NOVEMBER 2

• Hydrogen Spectra

• Balmer series

• Lyman Series

• Paschem Series


Bohr’s Model

• Niels Bohr adopted Planck’s assumption about energy and explained the hydrogen spectrum this way:

1. Only orbits of certain radii corresponding to certain definite energies are permitted for the electron in the hydrogen atom.


Bohr Model

• 2 An electron in a permitted orbit has a specific energy an is in an “allowed” energy state. It will not spiral into the nucleus

• 3 Energy is emitted or absorbed by the electron only as the electron changes from one allowed state to other


Hydrogen Line Spectrum

• The line spectrum for H has 4 lines in the visible region.

• Johan Balmer in 1885 showed that the wavelengths of these lines fit a simple formula. Later on additional lines were

found in the ultraviolet (Lyman series) and infrared (Pashem series)region. The equation was extended to a more general one that allowed the calculation of the wavelength for all lines of Hydrogen


Energy states of the Hydrogen Atom

The energy absorbed or emitted from the process of electron promotion or demotion can be calculated by the equation: E = −RH ( )1

nf2

1ni

2-

where RH is the Rydberg constant, 2.18 10−18 J, and ni and nf are the initial and final energy levels of the electron.


Balmer series

• If n=3 the wavelength of the red light in the Hydrogen Spectrum is obtained (656 nm)

• If n=4 the wavelength of the green line is calculated

• If n=5 and n=6 the equation give the wavelength for the blue lines


Balmer series. Visible range

• Electrons moving from states with n>2 to the n=2 state


Lyman Series

• Emission lines in the ultraviolet region.

• Electrons moving from states with n>1 to state=1


Paschem Series

• In the infrared area of the spectrum.

• From other energy levels to n = 1

• The largest jump, high energy, ultraviolet region.


Limitations of Bohr’s Model

• It does offer an explanation for the line spectrum of hydrogen, but it cannot explain other atoms.

• The two main contributions are that

a) Electrons exist only in certain energy levels.

b) If electrons move to another permitted energy level it must absorbed or emit energy as light.


Which is it?

• Is energy a wave like light, or a particle?

• Both! Concept is called the Wave -Particle duality.

• What about the other way, is matter a wave?

• Yes


The Wave Nature of Matter

• Louis de Broglie suggested that if light can have material properties, matter should exhibit wave properties.

• He demonstrated that the relationship between mass and wavelength was

=h

mv


Flame Test

• The flame test is used to visually determine the identity of an unknown metal or metalloid ion based on the characteristic color the salt turns the flame of a bunsen burner. The heat of the flame converts the metal ions into atoms which become excited and emit visible light. The characteristic emission spectra can be used to differentiate between some elements.


Flame Test Colors

• Li+ Deep red (crimson)• Na+ Yellow-orange• K+ Violet - lilac• Ca2+ Orange-red• Sr2+ Red• Ba2+ Pale Green• Cu2+ Green


Matter waves

• De Broglie described the wave characteristics of material particles.

• mv is the momentum • His equation is applicable to all matter,

however the wavelength associated with objects of ordinary size would be so tiny that could not be observed.

• Only for objects of the size of the electrons could be detected


The Uncertainty Principle

• Heisenberg showed that the more precisely the momentum of a particle is known, the less precisely is its position known:

• In many cases, our uncertainty of the whereabouts of an electron is greater than the size of the atom itself!

(x) (mv) h4


The Uncertainty Principle• Heisenberg’s Uncertainty Principle: on the mass scale

of atomic particles, we cannot determine exactly the position, direction of motion, and speed simultaneously.

• For electrons: we cannot determine their momentum and position simultaneously.

• If x is the uncertainty in position and mv is the uncertainty in momentum, then

4·

hmvx


5th Solvay Conference of Electrons and Photons - 1927


Quantum Mechanics

• Erwin Schrödinger developed a mathematical treatment into which both the wave and particle nature of matter could be incorporated.

• It is known as quantum mechanics.


Quantum Mechanics

• The wave equation is designated with a lower case Greek psi ().

• The square of the wave equation, 2, gives a probability density map of where an electron has a certain statistical likelihood of being at any given instant in time.


NOVEMBER 3

• QUANTUM MECHANICS AND ATOMIC ORBITALS

• ELECTRON CONFIGURATION.


Quantum Numbers

• Solving the wave equation gives a set of wave functions, or orbitals, and their corresponding energies.

• Each orbital describes a spatial distribution of electron density.

• An orbital is described by a set of three quantum numbers.


Principal Quantum Number, n

• The principal quantum number, n, describes the energy level on which the orbital resides.

• The values of n are integers ≥ 0.

• As n becomes larger, the electron is further from the nucleus.


Azimuthal Quantum Number, l(Angular momentum quantum #)

SUBSHELLS• This quantum number defines the

shape of the orbital.

• Allowed values of l are integers ranging from 0 to n − 1.

• We use letter designations to communicate the different values of l and, therefore, the shapes and types of orbitals.


Azimuthal or angular momentum Quantum Number, l

related to the type of orbitals

Value of l 0 1 2 3

Type of orbital s p d f


Magnetic Quantum Number, ml

• Describes the three-dimensional orientation of the orbital.

• Values are integers ranging from -l to l:

−l ≤ ml ≤ l.

• Therefore, on any given energy level, there can be up to 1 s orbital, 3 p orbitals, 5 d orbitals, 7 f orbitals, etc.


Magnetic Quantum Number, ml

• Orbitals with the same value of n form a shell.• Different orbital types within a shell are

subshells.


s Orbitals

• Value of l = 0.• Spherical in shape.• Radius of sphere

increases with increasing value of n.


The s-Orbitals• All s-orbitals are spherical.• As n increases, the s-orbitals get larger.• As n increases, the number of nodes increase.• A node is a region in space where the probability of

finding an electron is zero.• At a node, 2 = 0 • For an s-orbital, the number of nodes is (n - 1).


s Orbitals

Observing a graph of probabilities of finding an electron versus distance from the nucleus, we see that s orbitals possess n−1 nodes, or regions where there is 0 probability of finding an electron.


p Orbitals

• Value of l = 1.• Have two lobes with a node between them.


The p-Orbitals

• There are three p-orbitals px, py, and pz.

• The three p-orbitals lie along the x-, y- and z- axes of a Cartesian system.

• The letters correspond to allowed values of ml of -1, 0, and +1.

• The orbitals are dumbbell shaped.• As n increases, the p-orbitals get larger.• All p-orbitals have a node at the nucleus.


d Orbitals• Value of l is 2.• Four of the

five orbitals have 4 lobes; the other resembles a p orbital with a doughnut around the center.


Quantum numbers (4 numbers that determine the energy

of an electron)

• Principal quantum number (n) positive whole number

• Azimuthal or angular momentum quantum number (l) cannot be greater than n integer from 0 to n-1

• Magnetic quantum number (ml) integer from –l to +l

• Spin quantum number (ms) +1/2 or – 1/2


Electron Configuration of Excited Atoms

• They do not follow the proper fill out order. One or more electrons are at a higher energy level that what they are supposed to be.

• You need to spot the electron out of sequence to realize that the atom is in an excited state.


Energies of OrbitalsAUFBAU Diagram

• As the number of electrons increases, though, so does the repulsion between them.

• Therefore, in many-electron atoms, orbitals on the same energy level are no longer degenerate.


• http://inhttp://intro.chem.okstate.edu/WorkshopFolder/Electronconfnew.html

• http://intro.chem.okstate.edu/WorkshopFolder/Electronconfnew.html


Spin Quantum Number, ms

• In the 1920s, it was discovered that two electrons in the same orbital do not have exactly the same energy.

• The “spin” of an electron describes its magnetic field, which affects its energy.


Spin Quantum Number, ms

• This led to a fourth quantum number, the spin quantum number, ms.

• The spin quantum number has only 2 allowed values: +1/2 and −1/2.


Pauli Exclusion Principle

• No two electrons in the same atom can have exactly the same energy.

• For example, no two electrons in the same atom can have identical sets of quantum numbers.


Electron Configurations

• Distribution of all electrons in an atom

• Consist of Number denoting the

energy level



• Distribution of all electrons in an atom


energy level Letter denoting the type

of orbital



• Distribution of all electrons in an atom.


energy level. Letter denoting the type

of orbital. Superscript denoting the

number of electrons in those orbitals.


Orbital Diagrams

• Each box represents one orbital.

• Half-arrows represent the electrons.

• The direction of the arrow represents the spin of the electron.


Hund’s Rule• Electron configurations tells us in which orbitals the

electrons for an element are located.• Three rules:

• electrons fill orbitals starting with lowest n and moving upwards;

• no two electrons can fill one orbital with the same spin (Pauli);

• for degenerate orbitals, electrons fill each orbital singly before any orbital gets a second electron (Hund’s rule).


Condensed Electron Configurations• Neon completes the 2p subshell.• Sodium marks the beginning of a new row.• So, we write the condensed electron configuration for

sodium as

Na: [Ne] 3s1

• [Ne] represents the electron configuration of neon.• Core electrons: electrons in [Noble Gas].• Valence electrons: electrons outside of [Noble Gas].


Hund’s Rule

“For degenerate orbitals, the lowest energy is attained when the number of electrons with the same spin is maximized.”


Periodic Table

• We fill orbitals in increasing order of energy.

• Different blocks on the periodic table, then correspond to different types of orbitals.


Some Anomalies

Some irregularities occur when there are enough electrons to half-fill s and d orbitals on a given row.


Some Anomalies

For instance, the electron configuration for copper is

[Ar] 4s1 3d5

rather than the expected

[Ar] 4s2 3d4.


Some Anomalies

• This occurs because the 4s and 3d orbitals are very close in energy.

• These anomalies occur in f-block atoms, as well.


Transition Metals• After Ar the d orbitals begin to fill.• After the 3d orbitals are full, the 4p orbitals being to fill.• Transition metals: elements in which the d electrons

are the last electrons to fill.

Electron ConfigurationsElectron Configurations


Examples – Write electron configurations for the following:

1. Mg

2. N

3. Br

4. Cu

5. O


Lanthanides and Actinides• From Ce onwards the 4f orbitals begin to fill.• Note: La: [Xe]6s25d14f0

• Elements Ce - Lu have the 4f orbitals filled and are called lanthanides or rare earth elements.

• Elements Th - Lr have the 5f orbitals filled and are called actinides.

• Most actinides are not found in nature.


• The periodic table can be used as a guide for electron configurations.

• The period number is the value of n.• Groups 1 and 2 have the s-orbital filled.• Groups 13 - 18 have the p-orbitals filled.• Groups 3 - 12 have the d-orbitals filled.• The lanthanides and actinides have the f-orbital filled.

Electron Configurations Electron Configurations and the Periodic Tableand the Periodic Table


Equations

• Read Introduction to writing AP equations. Page xiii

• Review chapter 2, 3 Page 17 odd.

chapter 6 electronic structure of atoms

Documents

frequency of light

wavelength of light

particle nature of light

speed of light c

light shines

interaction of radiation

electromagnetic waves

threshold frequency