# lecture25

```Physics at the end of XIX Century
and
Major Discoveries of XX Century
Thompson’s experiment (discovery of electron)
Emission and absorption of light
Spectra:
•Continues spectra
•Line spectra
Three problems:
•“Ultraviolet catastrophe”
•Photoelectric effect
•Michelson experiment
1
Thompson’s experiment - discovery of electron (review)
Electron gun
Velocity selector

v
-

v
+
V
1
2
mv2  eV

B
+
-


F  0  v  const


 
E
F  qE  qv  B  0  v 
B
e
E2

m 2VB 2
2
Continues spectra and “Ultraviolet catastrophe”
Stefan-Boltzmann law
I  T 4
I   I  
Wien displacement law:
maxT  2.90103 m  K

Rayleigh’s law:
I   
2ckT
4
Plank’s law:
Plank’s constant:
34
h  6.62  10
J s
 4.14  1015 eV  s
2hc
I    5 hc kT
 e
1

E  hf

3
Example 1: What are the wavelength and the frequency corresponding to
the most intense light emitted by a giant star of surface temperature 5000 K?
maxT  2.90103 m  K
max  2.90  103 m  K / 5000K  0.580 106 m  580nm
f max  c / max  3  108 m / s / 0.580 106 m  5.2  1014 Hz
Example 2: What are the wavelength and 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6 m  7.77m
f max  c / max  3  108 m / s / 7.77  106 m  3.9  1013 Hz
4
Photoelectric effect
Experiment:
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
light
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
A
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
of electrons will increase linearly with frequency
• There is a cutoff frequency below which no electrons will be emitted,
regardless of intensity
5
light
Photoelectric effect (quantum theory)
Photons!
E  hf
A
1
2
Plank’s constant:
h  6.621034 J  s
2
mv max
 hf  W0
(1)
K max  E  W0
I
2
eV0  12 mvmax
 Kmax  eV0  hf-W0
(2)
V
-V0
V0 
V0
fmin
f
h W0
f hfmin  W0 ;
e
e
V0 h

f
e
6
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
W0  2.3eV
f  7.0 1014 Hz
V0  ?
hf  W0
eV0  hf-W0  V0 
e
4.14  1015 eV  s 7.0  1014 Hz  2.3eV
 0.6V
V0 
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 1014 Hz
W0  ?
hfmin  W0 



W0  4.14  1015 eV  s 7.5  1014 Hz  3.1eV
Copper, and iron will not emit electrons
7
Example: Rank the following radiations according to their associated
photon energies, greatest first:
(a) yellow light from a sodium vapor lamp
(b) a gamma ray emitted by a radioactive
(c) a radio wave emitted the antenna of a commercial radio station
(d) a microwave beam emitted by airport traffic control radar
Example: At what rate are photons emitted by a 100 W sodium vapor lamp if we
can assume the emission is entirely at a wave-length of 590 nm?
P  100W
  590nm
rate  P / E  ?
f 
c

E  hf 
hc




P P
100W   590109 m
rate  

E hc
6.631034 J  s 3.0 108 m / s



rate  3 1020 photons/ s
8
```