Applied Physics I: Chapter 7: Quantum Mechanics
Einstein's photo-electric equation
Einstein proposed a quantum theory on the basis that, "when a photon collides with an electron in a metal, it transfers the energy to the electron in an "all (or) none" process".
EINSTEIN'S PHOTO‒ELECTRIC
EQUATION
Einstein
proposed a quantum theory on the basis that, "when a photon collides with an electron in a metal, it transfers the
energy to the electron in an "all
(or) none" process", i.e., either the photon gives out its
total energy (hv) to the electron
(or) no energy is transferred to the electron.
According
to Einstein, the total energy of the photon, which is completely given to the
electron is used in two ways viz,
1.
A part of energy is used to eject the electron from the surface of the metal.
This energy is known as Photo‒electric
work function (ϕ).
2.
The other part of energy is supplied to the electron as the kinetic energy ( ½ mv2) for it to move with the
velocity 'v'.
∴ Total energy of the
photon (E) = ϕ + ½ mv2
Since
E=hy, we can write, hv = ϕ + ½ mv2 ………..(1)
Equation
(1) is called Einstein's photo‒electric
equation.
Special
Cases
Case (i):
Suppose if the energy of the incident photon is in such a way that it is used
only to eject the electron and not to make it move means, the kinetic energy of
the electron becomes zero.
∴ Equation (1) becomes, hv0=ϕ0 …………….(2)
where
v0
is called threshold frequency.
and
ϕ0 is the work function of the metal.
Case (ii):
Suppose if the energy of the incident photon ejects the electron and makes it
to move with maximum velocity (vmax) means, equation (1) becomes
hv = ϕ0 + ½ mv2max
Since
ϕ0 = hv0 we can
write
hv = hv0
+ ½ mv2max
(or)
hv
‒ hv0 = ½ mv2max
(or)
h(v ‒ v0)
= ½ mv2max …………….(3)
As
the work function is the energy supplied it is generally expressed in eV. The
work functions of some of the metals are listed below for reference.
Work
function for Metal
Cu:
4.30 eV
Fe:
4.74 eV
K:
1.90 eV
Na:
2.00 eV
Al:
3.00 eV
Applied Physics I: Chapter 7: Quantum Mechanics : Tag: Applied Physics : - Einstein's photo-electric equation
Applied Physics I: Chapter 7: Quantum Mechanics
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