# lecture25

```Physics at the end of XIX Century
and
Major Discoveries of XX Century
Thompson’s experiment (discovery of electron)

v
-

v
+

 B
-
+
V
1
2
mv
e
m

2
 eV
v
2
2V
v
E
B
e
m

E
2
2VB
2
Emission and absorption of light
Spectra:
•Continues spectra
•Line spectra
Three problems:
•“Ultraviolet catastrophe”
•Photoelectric effect
•Michelson experiment
Continues spectra and “Ultraviolet catastrophe”
I 
I  T
4
Wien displacement law:
 I  
 max T  2 . 90  10

3
mK
Rayleigh’s law:
I   
2  ckT

4
Plank’s law:
I   
2 hc
 e
5
hc  kT
1
Plank’s constant:
h  6 . 62  10
 34
J  s  4 . 14  10
 15
eV  s
E  hf

Example 1: What is the wavelength the frequency corresponding to the
most intense light emitted by a giant star of surface temperature 5000 K?
 max T  2 . 90  10
 max  2 . 90  10
3
3
mK
m  K / 5000 K  0 . 580  10
f max  c /  max  3  10 m / s / 0 . 580  10
8
6
6
m  580 nm
m  5 . 2  10
14
Hz
Example 2: What is the wavelength the frequency of the most intense
radiation from an object with temperature 100&deg;C?
 max  2 . 90  10
3
m  K /  273  100  K  7 . 77  10
f max  c /  max  3  10 m / s / 7 . 77  10
8
6
6
m  3 . 9  10
m  7 . 77  m
13
Hz
Photoelectric effect
light
Experiment:
A
If light strikes a metal, electrons are emitted. The effect
does not occur if the frequency of the light is too low; the
kinetic energy of the electrons increases with frequency.
Classical theory can not explain these results.
If light is a wave, classical theory predicts:
• Frequency would not matter
• Number of electrons and their energy should increase with intensity
Quantum theory:
Einstein suggested that, given the success of Planck’s theory, light must be
emitted and absorbed in small energy packets, “photons” with energy: E  hf
If light is particles, theory predicts:
• Increasing intensity increases number of electrons but not energy
• Above a minimum energy required to break atomic bond, kinetic energy will
increase linearly with frequency
• There is a cutoff frequency below which no electrons will be emitted,
regardless of intensity
light
Photoelectric effect (quantum theory)
Photons!
Plank’s constant:
E  hf
A
1
2
h  6 . 62  10
34
J s
mv max  hf  W 0
2
(1)
K max  E  W 0
I
eV 0 
1
2
mv max  K max

2
eV 0  hf-W
0
V
-V0
V0
V0 
 V0
f
fmin
f
h
f-
e

W0
e
h
e

hf min  W 0
Photons:
E  pc  hf - energy
p 
hf
c

h

- momentum
(2)
Example: The work function for a certain sample is 2.3 eV. What is the
stopping potential for electrons ejected from the sample by 7.0*1014 Hz
W 0  2 . 3 eV
f  7 . 0  10
14
eV 0  hf-W
Hz
V0  ?
V0 
0
 V0 
4 . 14  10
 15
hf  W 0
e
eV  s 7 . 0  10
14
Hz   2 . 3 eV
 0 . 6V
1e
Example: The work function for sodium, cesium, copper, and iron are 2.3, 2.1,
4.7, and 4.5 eV respectively. Which of these metals will not emit electrons
when visible light shines on it?
f  7 . 5  10
W0  ?
14
Hz
hf min  W 0 
W 0  4 . 14  10
 15
eV  s 7 . 5  10
14
Copper, and iron will not emit electrons
Hz   3 . 1eV
```