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Introduction to Modern Physics
A (mainly) historical perspective on
- atomic physics

- nuclear physics
- particle physics
Theories of
Blackbody
Radiation
Classical
disaster !
Quantum
solution
Planck’s “Quantum Theory”
I  , T  

5
 hckT 
 e  1




The “oscillators” in
the walls can only
have certain
energies – NOT
continuous!
The Photoelectric Effect
Light = tiny particles!
Wave theory: takes too long to get enough
energy to eject electrons
Particle theory: energy is concentrated in
packets -> efficiently ejects electrons!
The Photoelectric Effect
Energy of molecular oscillator, E = nhf
Emission: energy nhf -> (n-1)hf
 Light emitted in packet of energy
E = hf
Einstein’s prediction:
hf = KE + W (work function)
c = f
Frequency
Speed of light
3 x 108
meter/second
or
30cm (1 foot)
per nanosecond
Wavelength
(meter)
#vibrations/
second
hf = KE + W (work function)
The Photoelectric Effect
Photon Theory
Wave Theory
Increase light intensity ->
Increase light intensity ->
more electrons with more KE
more photons -> more electrons

Frequency of light does not
affect electron KE
X
X
but max-KE unchanged !
Max-KE = hf - W
If f < f(minimum) ,
where hf(minimum) = W,



Then NO electrons are emitted!
How many photons from a lightbulb?
100W lightbulb, wavelength = 500nm
Energy/sec = 100 Joules
E = nhf ->

n=
n = E/hf = E/hc
100J
x
500 x 10-9
6.63 x 10-34 J.s x 3 x 108 m/s
= 2.5 x 1020 !!
So matter contains electrons and light
can be emitted in “chunks”… so what
does this tell us about atoms??
Possible models of the atom
Which one is correct?
The Rutherford Experiment
Electric potential
V(r) ~ 1/r
Distance of closest approach ~ size of nucleus
At closest point KE -> PE, and PE = charge x potential
KE = PE = 1/40 x 2Ze2/R
R = 2Ze2/ (40 x KE) = 2 x 9 x 109 x 1.6 x 10-19 x Z
1.2 x 10-12 J
= 3.8 x 10-16 Z meters = 3.0 x 10-14 m for Z=79 (Gold)
The “correct” model of the atom
…but beware of simple images!
Atomic “signatures”
Rarefied gas
Only discrete lines!
1 
 1
 R 2  2 

2 n 
1
1 
 1
 R 2  2 

2 n 
1
An empirical formula!
n = 3,4,…
The Origin of Line Spectra
Newton’s 2nd Law and Uniform Circular
Motion
F = ma
Acceleration = v2/r
Towards center of
circle!
How do we get “discrete energies”?
Angular momentum
L = mvr
Radius r
Linear momentum = mv
Bohr’s “quantum” condition –
motivated by the Balmer formula
h
L  mvrn  n
2
n  1,2,3,...
Electron “waves” and the Bohr condition
De Broglie(1923):
 = h/mv
Only waves with a
whole number of
wavelengths persist
n = 2r
Same!!
h
L  mvrn  n
2
Quantized orbits!
Electrostatic force: Electron/Nucleus
COULOMBS LAW
Combine Coulomb’s Law with the Bohr condition:
Newton’s 2nd Law
Circular motion
1 ( Ze)e mv 2

2
40 rn
rn
F  ma
2
v
a
r

h
L  mvrn  n
2
nh
v
2mrn
n h 0 n
rn 
 r1
2
mZe
Z
2
2
2
h 0
(6.626 x10 )(8.85 x10 )
r1 

2
31
19
me (3.14)(9.11x10 )(1.602 x10 )
34
2
 0.529 x10
10
m
(for Z = 1, hydrogen)
12
Calculate the total energy for the electron:
Total Energy = Kinetic + Potential Energy
Electrostatic
potential
Electrostatic
potential
energy
1 Q
1 Ze
V

40 r 40 r
1
Ze
U  eV  
40 r
2
Total energy
1 2
1 Ze 2
En  mv 
2
40 rn
Substitute
 Z 2e 4 m  1  Z 2
En   2 2  2   2 E1
 8 0 h  n  n
4
me
E1  
 2.17 x10  18 Joules  13.6eV
2
8 0 h
 13.6eV
En 
2
n
So the energy is quantized !
… now we can combine this with
hf  Eu  El
hf 
hc

1
Z e m 1
1
  En  E '  
 2
3 
2
 hc
8 0 h c  n' n 
1
2 4
…and this correctly predicts the line
spectrum for hydrogen,
…and it gets the Rydberg constant R
right!
…however, it does not work for more
complex atoms…
Experimental results
Quantum Mechanics – or how the atomic
world really works (apparently!)
Take the wave description
of matter for real:
De Broglie(1923):
 = h/mv
Describe e.g. an electron
by a “wavefunction” (x),
then this obeys:
h d

 U ( x) ( x)  E ( x)
2
2m dx
2
2
Schroedinger’s famous equation
Now imagine we
confine an electron
in a “box” with
infinitely hard/high
walls:
Waves must end at the
walls so:
and the energy levels for these states
are:
Discrete energies!
The probabilities for the electron to
be at various places inside the box are:
vs. Classical
Mechanics
Uniform probability!
Applying the same quantum mechanical
approach to the hydrogen atom:
Probability
“cloud”
Bohr radius
The “n = 2” state of hydrogen:
Atomic orbitals
Weird stuff!!
Weird stuff!!
Ghosts!!??
Conclusions
- Classical mechanics/electromagnetism
does not describe atomic behavior
- The Bohr model with a “quantum condition”
does better…but only for hydrogen
- Quantum mechanics gives a full description
and agrees with experiment
- …but QM is weird!!