By Team Aakash Byju's | 29th January 2023
λ =
An electromagnetic wave of wavelength λ is incident on a photosensitive surface of negligible work function. If the photoelectrons emitted from this surface have the de Broglie wavelength λ', then
-1
2
mc
λ'
h
λ =
2
3mc
λ'
2h
λ =
2
2mc
λ'
h
λ =
2
5mc
λ'
h
Detailed Explanation
λ =
2
2mc
λ'
h
According to Einstein’s photoelectric equation, the maximum kinetic energy is given as
KE =hv-O
max
Where,
h - Planck’s constant
v - frequency of the incident wave
O - work function of the surface
o
o
Since it is given that the work function of the surface is negligible and the kinetic energy is also written as
Where,
KE = mv
1
2
2
m and v are the mass & velocity of electrons
Also, the expression of the frequency is
v =
Where,
c is the speed of light and
c
λ
λ is the wavelength
We also know that momentum can be expressed as p = mv.
KE =hv-O
max
o
=>
mv
1
2
2
= h
c
λ
=>
1
2m
(mv)
2
= h
c
λ
=>
1
2m
p
2
= h
c
λ
Further, the momentum can also be expressed in terms of the de Broglie wave of wavelength λ′.
p =
h
λ'
. .
1
2m
p
2
= h
c
λ
=>
1
2m
h
c
λ =
( )
h
λ'
2
= h
c
λ
2mλ'
=>
h
2
=
c
λ
=>
2mλ'
2
.