3/29/2012

1

Chapter 7

Electronic Structure of Atoms

Electromagnetic Radiation

• You should – Know visible range (400 – 700 nm)

– Know UV is of lower wavelength (higher energy)

– Know IR is of higher wavelength (lower energy)

3/29/2012

2

Wavelength and Frequency

• Wavelength (): Distance between crests.

– Units usually in nm (10-9 m)

• Frequency (): Number of crests passing in a given time.

– Units are in Hz (s-1)

• = c/ • c = speed of light

• 3.00 x 108 m/s

Photoelectric Effect

• Shine light on a metal

– High wavelength: no electrons emitted

– Low wavelength: electrons emitted

• Classical physics could not explain this behavior

3/29/2012

3

Photoelectric Effect

• Einstein – Light consists of particles

called photons

– Photon energy: E = hν = hc/λ • High wavelength photons

have low energy

• Low wavelength photons have high energy

– Low wavelength photons have enough energy to knock electrons from metal

• Note: I won’t ask for calculations as on p 281-282 of text

(Example 7.3)

Quantum Theory

• Models behavior of small particles

• Extends Einstein’s photon model of light

• Original atomic model: Bohr (1913)

– Planetary model

– Nucleus in center

– Electrons in orbits

3/29/2012

4

Bohr Model of Hydrogen Atom

• Electrons in H atom only have certain allowed energies (corresponding to orbits) – Called energy levels

– RH = 2.179 x 10-18 J

• E = 0 when electron is separated from atom

• You should know the formula above – Don’t memorize value of RH

Bohr Model

• Bohr model for H atom worked well

• Made predictions that matched experimental results

– Ionization energy • Energy required to remove an electron from an atom

– Spectroscopy • Interaction of atoms and molecules with light

3/29/2012

5

Ionization Energy

• Ionization energy = energy required to remove an electron from an atom

• Bohr’s model prediction:

– Most H atoms in lowest energy level (ground state)

– Ionization energy of H atom is RH = 2.179 x 10-18 J

• Matches experiment

Electronic Spectroscopy

• Certain wavelengths of light are absorbed by atoms and molecules

– Pushes electron up to another energy level

• Electrons also can fall from higher level to a lower, emitting light

3/29/2012

6

Electronic Spectroscopy

• What wavelength of light would cause the absorption transition shown below?

– RH = 2.179 x 10-18 J

– E = hc/

– h = 6.626 x 10-34 J s

– c = 3.00 x 108 m/s

– Don’t memorize values of RH, h, or C

• Agrees with experiment

Bohr Model

• Works well for H atom

• Physicists could not extend it to atoms with more than one electron

• Another theory soon arose: quantum mechanics

3/29/2012

7

Wave-Particle Model

• Already established: waves can be modeled as particles

• New idea: Small particles can be modeled as waves

• Remember Einstein: E = hc/λ

• Also from Einstein: E = mc2

Wave-Particle Model

• de Broglie: particles have a wavelength

– E = hc/λ = mc2

– λ = h/mc

• λ = h/mu

– u = speed < speed of light

3/29/2012

8

Microscopes

• Ordinary microscope

– Light is disturbed by subject, focused by lens and viewed

• UV and visible light

– Wavelengths: 150 – 720 nm

• Won’t work for a really small object

– Won’t disturb light enough to be detectable

– Also diffraction problems

Electron Microscope

• Electrons have a wavelength λ = h/mu

– h = 6.63 x 10-34 J s J = kg.m2/s2 (don’t memorize)

– m = 9.1 x 10-31 kg (don’t memorize)

– u = 1.8 x 108 m/s (near highest value of electron speed)

– λ = 4.0 x 10-12 m = 0.004 nm – Much smaller than visible light (150 – 720 nm)

• Electron microscope

– Can see smaller objects

3/29/2012

9

Quantum Mechanics

• Developed by Erwin Schrödinger in 1926

• Another contributor: Werner Heisenberg

– Both Nobel Prize winners in 1933 and 1932

• Basic premise: small particles are wavelike

Heisenberg Uncertainty Principle

• x px > h/4 – = uncertainty x = position px = momentum (mu)

• Consequence of wave nature of matter.

• Can’t tell simultaneously exactly where a particle is and how fast it is going. – The more precisely you measure one property, the less

precisely you know the other.

• Quantum Theory only gives the probability of finding a particle at a particular position.

3/29/2012

10

Quant. Mech. Model of Atoms

• Each electron is labeled by four quantum numbers

– n: 1, 2, 3, . . . .

– l: 0, 1, 2, . . . n-1

– ml: 0, ±1, . . . ±l

– ms: ± ½

• For a given value of n, only certain quantum numbers are possible

– n = 1; l = 0; ml = 0; ms = ± ½

– n = 2: l = 0; ml = 0; ms = ± ½ n = 2; l = 1; ml = 0, ± 1; ms = ± ½

Quantum Numbers

• The quantum numbers of an electron in an atom tell us about its properties

– How far the electron is from the nucleus on the average

– Where there is a high probability of finding it

– Its possible energies

3/29/2012

11

Quantum Numbers: Orbitals

• The l quantum number tells the orbital an e- is in

– Region in which there is high probability of finding e-

l = 0: s-orbital l = 1: p-orbital (three orbitals) l = 2: d-orbital (five orbitals)

Quantum Numbers: Orbitals

• For a given value of n, only certain orbitals exist

– n = 1: l = 0 1s

– n = 2: l = 0, 1 2s, 2p

– n = 3: l = 0, 1, 2 3s, 3p, 3d

• Orbitals differing only in orientation have the same energy -- subshells

– p-subshell: three p-orbitals (px, py, pz)

– d-subshell: five d-orbitals

– f-subshell: seven f-orbitals

3/29/2012

12

Quantum Numbers: Atomic Size

• Average distance of electrons from nucleus is higher for higher n quantum numbers

Probability

Distance from nucleus

Quantum Numbers

• Compare a 2p electron with a 3p electron

– Possible quantum numbers

– Distance from nucleus on average

– Shape of high-probability region

3/29/2012

13

Quantum Numbers: Energy Levels

• Energies of electrons in multi-electron atoms depend on both n and l quantum numbers.

4p n = 4 l = 1 3d n = 3 l = 2 4s n = 4 l = 0 3p n = 3 l = 1 3s n = 3 l = 0 2p n = 2 l = 1 2s n = 2 l = 0

1s n = 1 l = 0

Multi-Electron Atoms

• H atom: Electronic energies only depend on n

• Multi-electron atoms: Electronic energies depend on n and l

• Why the difference?

H atom Multi-electron atoms

3/29/2012

14

Multi-Electron Atoms: Shielding

• Electrons close to nucleus shield positive charge from outer electrons

• Li atom – Nuclear charge = +3

– Two 1s electrons and one 2s electron

• 2s electrons on average are farther from nucleus than 1s – 1s electrons shield 2s from +3 charge

– 2s electrons feel less than +3

– 1s electrons feel approximately +3

Shielding and Penetration

• Compare 2s and 2p electrons

• 2s have small bump of high probability inside 1s

– 2s orbital “penetrates” 1s

• 2s electrons attracted to nucleus more than 2p

• 2s electrons lower energy than 2p

3/29/2012

15

Shielding and Penetration

• 4s electrons have lower energy than 3d

• 4s electrons penetrate 3d

– 4s electrons held more tightly by positive nucleus and hence are of lower energy

Box Diagrams

• Easy way to remember relative energies of different orbitals

3/29/2012

16

Electron Configurations

Build up electron configurations of atoms by feeding them into lowest possible energies. Must be consistent with two principles: 1. Pauli Exclusion Principle 2. Hund’s Rule

Pauli Exclusion Principle

• No two electrons in same atom can have same four quantum numbers

• Requires that electron in same orbital have different spins.

n, l, and ml quantum numbers same. ms quantum numbers must be different

3/29/2012

17

Paired and Unpaired Electrons

• Paired electrons: in same orbital with different spins

• Unpaired electrons: single electron in an orbital

Subshells

• Set of equivalent orbitals

• Three 3p orbitals for example

• Energies of orbitals in a subshell are the same

• All of the following arrangements are equivalent

3/29/2012

18

Hund’s Rule

• The most stable arrangement of electrons in subshells has the greatest number of parallel spins

– Fill empty orbitals in a subshell first

– Keep spins parallel

– Put two electrons in same orbital only when there are no empty orbitals in the subshell

or

Electron Configuration

• Write box diagram ground-state electron configurations for C, P, Fe

3/29/2012

19

Electron Configurations

• What is the problem with each ground-state electron config. shown here?

Electron Configurations

• Frequently use superscript to represent number of electrons in a subshells

• C 1s22s22p2

• Fe

• 1s22s22p63s23p64s23d6

3/29/2012

20

Electron Configurations

• Use diagram at right as guide

• What is ground-state e- conf. of Argon? – Z = 18

• What is ground-state e- conf. of Vanadium – Z = 23

• Can write V e- conf. as [Ar]4s23d3

Electron Configurations

• An electron is in a 3p orbital. What are its possible quantum numbers?

• How many p-electrons are there in oxygen? How many are unpaired?

• What is wrong with the ground-state electron configurations below?

– 1s22s22p73s2

– 1s22s22p53s2

3/29/2012

21

Electron Configurations

• There are a few irregularities because

– Half-filled (d5) and filled (d10) d-orbitals have special stability

– 4s and 3d energies are close

• Chromium (Z = 24): [Ar] 4s13d5 NOT [Ar] 4s23d4

• Copper (Z = 29): [Ar] 4s13d10 NOT [Ar] 4s23d9

Magnetism

• Paramagnetism: weak attraction to magnetic field

– Characteristic of net unpaired electrons

– Strength of paramagnetism tells number of unpaired e-

• Diamagnetism: very weak repulsion by magnetic field

– All electrons paired

• Can use e- config to predict magnetism of atom

– Be (Z = 4): 1s22s2 Diamagnetic or paramagnetic?

– N (Z = 7): 1s22s22p3 Diamagnetic or paramagnetic?