Dr.Eman Zakaria Hegazy Quantum Mechanics and Statistical Thermodynamics Lecture3
Photoelectric effect
Photoelectric effect: a phenomenon in which electrons are
ejected from the surface of some metals exposed to light of at
least a certain minimum frequency, called the threshold
frequency.
- The number of electrons ejected was proportional to the
intensity of the light.
- Below the threshold frequency no electrons were ejected.
-
The photoelectric effect could not be explained by the
wave theory of light.
- If the potential is continuously increased, the electrons will
be stopped completely and potential needed to do that
called the stopping potential.
- At the stopping potential, the initial kinetic energy of the
electrons is equal the potential energy.
½ mv2= - e Vs
(1- 10)
Where Vs: is the stopping potential
e: is a negative number
1
Dr.Eman Zakaria Hegazy Quantum Mechanics and Statistical Thermodynamics Lecture3
Einstein explained the photoelectric effect with a quantum
hypothesis
- Einstein appealed to Planck’s hypothesis but extended it in
an important way
- Planck had applied his energy quantization concept,
  h.
, Planck believed that once the light energy was emitted
it behaved like a classical wave.
- Einstein proposed instead that the radiation itself existed
as small packets of energy ,
photons.
  h . ,
which are known as
- Einstein showed that the kinetic enrgy of the ejected
electrons ½ mv2 is equal to the energy of the incident
radiation h. minus energy required to remove an electron
from the surface of particular metal () .
1
m .v 2  h .  
2
(1-11)
2
Dr.Eman Zakaria Hegazy Quantum Mechanics and Statistical Thermodynamics Lecture3
Where  called the work function of the metal , is similar to
an ionization energy.
Suppose that
h .  
h . o  
(1-12)
Where o : threshold frequency is the minimum frequency that
will eject an electron is just a frequency required to overcome
the work function off the metal.
Using equations (1-10) and (1-12) we can write (1-11) as
eV s  h .  h . o
One electron volt = (1 coulomb)× (1 volt) = 1 joul
1eV= (1.602×10-19 C)(1 V)
= 1.602×10-19 J
3
Dr.Eman Zakaria Hegazy Quantum Mechanics and Statistical Thermodynamics Lecture3
Example 4:
Given that the work function for sodium metal is 1.82 eV, what
is the threshold frequency?
Solution:
We must first convert  from electron volt to jouls
1.602 1019
)  2.92 1019 J
= 1.82 eV = (1.82eV )(
eV
.
From Eq. (1-12) h .o= 
h: Planck’s constant: 6.626 × 10-34 J.S

2.92 1019 J
14
1
o  

4.40

10
(
S
)
34
h 6.626 10 J / S
=4.40×1014 Hz
Because Hz= S-1
4
Dr.Eman Zakaria Hegazy Quantum Mechanics and Statistical Thermodynamics Lecture3
Example (5):
When Lithium is irradiated with light , one finds a stopping
o
potential of 1.83 V for =3000 A . From these data and known
charge on the electron find (a) Plancks’s constant (b) the threshold
potential and (c) the work function of lithium
Solution:
c
(a) From eq. (1-13) and  

e (V 1 V 2 )  h .( 1  2 )  h .c (
1
1

1
2
)
1
1
e (1.83  0.80)  h  3  10 (

)
10
10
3000 10
4000 10
8
e (1.03V )  h .(2.5 1014 Hz )
h
1.03V
15
1


4.12

10
J
.
S
.
C
e 2.5 1014
h  (4.12 1015 )  (1.602 1019 )
=6.60×10-34J.S
5
Dr.Eman Zakaria Hegazy Quantum Mechanics and Statistical Thermodynamics Lecture3
(b)
Using =3000Å
eV s  h .  h . o
h.
(1.602×10-19C)(1.83 V)=
c
 h . o
10
3000 10 m
6.63 1034  3 108
 h . o
7
2.93×10-19=
3 10
h . o  6.63 1019  2.93 1019
h . o  3.7 1019
3.7 1019
14
o 

5.57

10
Hz
34
6.63 10
(c)
  h . o  3.7 1019 J
to convert to eV divide on 1.602×10-19
3.7 1019

 2.3 eV
19
1.602 10
6