CBSE Class 12 Physics 2015 Delhi Set 1 Paper

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Question : 13
Total: 26
Write Einstein's photoelectric equation and mention which important features in photoelectric effect can be explained with the help of this equation.
The maximum kinetic energy of the photoelectrons gets doubled when the wavelength of light incident on the surface changes from λ1 to λ2. Derive the expressions for the threshold wavelength λ0 and work function for the metal surface.
Solution:  
(i) Einstein's Photoelectric equation
(ii) Important features
(iii)Derivation of expressions for λ0 and work function
hv=ϕ0+kmax
or hv=hv0+
1
2
m
v2
max

Important features
(i) kmax depends linearly on frequency v.
(ii) Existence of threshold frequency for the metal surface.
(Any other two correct features.)
hv=ϕ0+kmax
hc
λ1
=
hc
λ0
+kmax
......(i)
hc
λ2
=
hc
λ0
+2kmax
......(ii)
From (i) and (ii)
2hc
λ1
hc
λ2
=
hc
λ0

1
λ0
=(
2
λ1
1
λ2
)

λ0=
λ1λ2
2λ2λ1

Work function ϕ0=
hc
λ0
=
hc(2λ2λ1)
λ1λ2
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