1. ATOMIC STRUCTURE Kotz Ch 7 & Ch 22 (sect 4,5)
properties of light
spectroscopy
quantum hypothesis
hydrogen atom
Heisenberg Uncertainty Principle
orbitals

2. ELECTROMAGNETIC RADIATION
subatomic particles (electron, photon, etc) have both PARTICLE and WAVE properties
Light is electromagnetic radiation - crossed electric and magnetic waves:
Properties :
Wavelength, l (nm)
Frequency, n (s-1, Hz)
Amplitude, A
constant speed. c
3.00 x 108 m.s-1

3. Electromagnetic Radiation (2)

4. Electromagnetic Radiation (3)
All waves have: frequency and wavelength
symbol: n (Greek letter “nu”) l (Greek “lambda”)
units: “cycles per sec” = Hertz “distance” (nm)
All radiation: l • n = c
where c = velocity of light = 3.00 x 108 m/sec
Note: Long wavelength
 small frequency
Short wavelength
 high frequency
increasing
wavelength
frequency

5. Electromagnetic Radiation (4)
Example: Red light has l = 700 nm.
Calculate the frequency, n. =
3.00 x 10 8
m/s
7.00 x 10 -7 m
4.29 x 10 14 Hz
n = c l
Wave nature of light is shown by classical wave properties such as
interference
diffraction

6. Quantization of Energy
Max Planck ( )
Solved the “ultraviolet
catastrophe”
4-HOT_BAR.MOV
Planck’s hypothesis: An object can only gain or lose energy by absorbing or emitting radiant energy in QUANTA.

7. Quantization of Energy (2)
Energy of radiation is proportional to frequency.
E = h • n
where h = Planck’s constant = x J•s
Light with large l (small n) has a small E.
Light with a short l (large n) has a large E.

8. Photoelectric Effect Albert Einstein (1879-1955)
Photoelectric effect demonstrates the
particle nature of light. (Kotz, figure 7.6)
No e- observed until light
of a certain minimum E is used.
Number of e- ejected does NOT
depend on frequency, rather it
depends on light intensity.

9. Photoelectric Effect (2)
Classical theory said that E of ejected
electron should increase with increase
in light intensity — not observed!
Experimental observations can be explained if light consists of particles called PHOTONS of discrete energy.

10. Energy of Radiation
PROBLEM: Calculate the energy of 1.00 mol of photons of red light.
l = 700 nm n = x 1014 sec-1
E = h•n
= (6.63 x J•s)(4.29 x 1014 sec-1)
= x J per photon
E per mol = (2.85 x J/ph)(6.02 x 1023 ph/mol)
= kJ/mol
- the range of energies that can break bonds.

11. Atomic Line Spectra
Bohr’s greatest contribution to science was in building a simple model of the atom.
It was based on understanding the SHARP LINE SPECTRA of excited atoms.
Niels Bohr ( )
(Nobel Prize, 1922)

12. Line Spectra of Excited Atoms
Excited atoms emit light of only certain wavelengths
The wavelengths of emitted light depend on the element. H Hg Ne

13. Atomic Spectra and Bohr Model
One view of atomic structure in early 20th century was that an electron (e-) traveled about the nucleus in an orbit.
1. Classically any orbit should be
possible and so is any energy.
2. But a charged particle moving in an electric field should emit energy.
End result should be destruction!

14. Atomic Spectra and Bohr Model (2)
Bohr said classical view is wrong.
Need a new theory — now called QUANTUM or WAVE MECHANICS.
e- can only exist in certain discrete orbits
— called stationary states.
e- is restricted to QUANTIZED energy states.
Energy of state = - C/n2 where
C is a CONSTANT
n = QUANTUM NUMBER, n = 1, 2, 3, 4, ....

15. Atomic Spectra and Bohr Model (3)
Energy of quantized state = - C/n2
Only orbits where n = integral number are permitted.
Radius of allowed orbitals
= n2 x ( nm)
Results can be used to
explain atomic spectra.

16. Atomic Spectra and Bohr Model (4)
If e-’s are in quantized energy states, then DE of states can have only certain values. This explains sharp line spectra.
H atom
07m07an1.mov
n = 1
n = 2
E = -C (1/22)
E = -C (1/12)
4-H_SPECTRA.MOV

17. Atomic Spectra and Bohr Model (5).
Atomic Spectra and Bohr Model (5) n = 1 2
Energy
Calculate DE for e- in H “falling” from
n = 2 to n = 1 (higher to lower energy) .
DE = Efinal - Einitial = -C[(1/12) - (1/2)2] = -(3/4)C
(-ve sign for DE indicates emission (+ve for absorption)
since energy (wavelength, frequency) of light can only be +ve it is best to consider such calculations as DE = Eupper - Elower
C has been found from experiment. It is now called R,
the Rydberg constant. R = 1312 kJ/mol or 3.29 x 1015 Hz
so, E of emitted light = (3/4)R = x 1015 Hz
and l = c/n = nm (in ULTRAVIOLET region)
This is exactly in agreement with experiment!

18. n En = -1312 n2 High E Short l High n Low E Long l Low n
Hydrogen atom spectra
Visible lines in H atom
spectrum are called the
BALMER series. 6 5 3 2 1 4 n
Energy
Ultra Violet
Lyman
Visible
Balmer
Infrared
Paschen
En = -1312 n2

19. From Bohr model to Quantum mechanics
Bohr’s theory was a great accomplishment and radically changed our view of matter.
But problems existed with Bohr theory —
theory only successful for the H atom.
introduced quantum idea artificially.
So, we go on to QUANTUM or WAVE MECHANICS

20. Quantum or Wave Mechanics
Light has both wave & particle properties
de Broglie (1924) proposed that all moving objects have wave properties.
For light: E = hn = hc / l
For particles: E = mc2 (Einstein)
L. de Broglie
( )
Therefore, mc = h / l
and for particles
(mass)x(velocity) = h / l
l for particles is called the de Broglie wavelength

21. WAVE properties of matter
Na Atom Laser beams
l = 15 micometers (mm)
Andrews, Mewes, Ketterle
M.I.T. Nov 1996
The new atom laser emits pulses of coherent atoms,
or atoms that "march in lock-step." Each pulse
contains several million coherent atoms and
is accelerated downward by gravity. The curved
shape of the pulses was caused by gravity and forces
between the atoms. (Field of view 2.5 mm X 5.0 mm.)
WAVE properties of matter
Electron diffraction with
electrons of keV
- Fig Al metal
Davisson & Germer 1927
4-ATOMLSR.MOV

22. Quantum or Wave Mechanics
Schrodinger applied idea of e- behaving as a wave to the problem of electrons in atoms.
Solution to WAVE EQUATION gives set of mathematical expressions called
WAVE FUNCTIONS, Y
Each describes an allowed energy state of an e-
Quantization introduced naturally.
E. Schrodinger

23. WAVE FUNCTIONS, Y • Y is a function of distance and two angles.
• For 1 electron, Y corresponds to an ORBITAL — the region of space within which an electron is found.
• Y does NOT describe the exact location of the electron.
• Y2 is proportional to the probability of finding an e- at a given point.

24. Uncertainty Principle
Problem of defining nature of electrons in atoms solved by W. Heisenberg.
Cannot simultaneously define the position and momentum (= m•v) of an electron.
Dx. Dp = h
At best we can describe the position and velocity of an electron by a
PROBABILITY DISTRIBUTION, which is given by Y2
W. Heisenberg

25. Y2 is proportional to the probability
Wavefunctions (3)
Y2 is proportional to the probability
of finding an e- at a given point.
4-S_ORBITAL.MOV
(07m13an1.mov)

26. Orbital Quantum Numbers
An atomic orbital is defined by 3 quantum numbers:
n l ml
Electrons are arranged in shells and subshells of ORBITALS .
n  shell
l  subshell
ml  designates an orbital within a subshell

27. Symbol Values Description
Quantum Numbers
Symbol Values Description
n (major) 1, 2, 3, .. Orbital size and
energy = -R(1/n2)
l (angular) 0, 1, 2, .. n-1 Orbital shape or
type (subshell)
ml (magnetic) -l..0..+l Orbital orientation
in space
Total # of orbitals in lth subshell = 2 l + 1

28. Shells and Subshells For n = 1, l = 0 and ml = 0
There is only one subshell and that subshell has a single orbital
(ml has a single value ---> 1 orbital)
This subshell is labeled s (“ess”) and we call this orbital 1s
Each shell has 1 orbital labeled s.
It is SPHERICAL in shape.

29. s Orbitals
All s orbitals are spherical in shape.

30. p Orbitals
Typical p orbital
For n = 2, l = 0 and 1
There are 2 types of orbitals — 2 subshells
For l = 0 ml = 0
this is a s subshell
For l = 1 ml = -1, 0, +1
this is a p subshell with 3 orbitals
planar node
When l = 1, there is a PLANAR NODE through the nucleus.

31. p orbitals (2)
The three p orbitals lie 90o apart in space
A p orbital

32. px py pz
l =
p-orbitals(3) n= 2 3

33. d Orbitals l = 0, 1, 2 For l = 1, ml = -1, 0, +1
For n = 3, what are the values of l?
l = 0, 1, 2
and so there are 3 subshells in the shell.
For l = 0, ml = 0
 s subshell with single orbital
For l = 1, ml = -1, 0, +1
 p subshell with 3 orbitals
For l = 2, ml = -2, -1, 0, +1, +2
 d subshell with 5 orbitals

34. d Orbitals IN GENERAL the number of NODES = value of angular
typical d orbital
planar node
s orbitals have no planar node (l = 0) and so are spherical.
p orbitals have l = 1, and have 1 planar node,
and so are “dumbbell” shaped.
d orbitals (with l = 2)
have 2 planar nodes
IN GENERAL
the number of NODES
= value of angular
quantum number (l)

35. Boundary surfaces for all orbitals of the n = 1, n = 2 and n = 3 shells
There are n2
orbitals in
the nth SHELL 2 1

36. ATOMIC ELECTRON CONFIGURATIONS AND PERIODICITY

37. Element Mnemonic Competition
Hey! Here Lies Ben Brown. Could Not Order Fire. Near
Nancy Margaret Alice Sits Peggy Sucking Clorets. Are
Kids Capable ?
WHAT’s YOURs ??