CBSE Class 12 Physics 2015 Delhi Set 1 Paper

Question : 13 of 26

Marks: +1, -0

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

λ_1

λ_2

. Derive the expressions for the threshold wavelength

λ_0

and work function for the metal surface.

Solution:

(i) Einstein's Photoelectric equation
(ii) Important features
(iii)Derivation of expressions for

λ_0

and work function

\;h v=ϕ_0+k_{\max }

\;h_v=h v_0+\;{1}/{2} m v^2 \max

Important features
(i)

k_{\max }

depends linearly on frequency

v

.
(ii) Existence of threshold frequency for the metal surface.
(Any other two correct features.)

\;h v=ϕ_0+k_{\max }

\;\;{h c}/{λ_1}=\;{h c}/{λ_0}+k_{\max }

......(i)

\;\;{h c}/{λ_2}=\;{h c}/{λ_0}+2 k_{\max }

......(ii)
From (i) and (ii)

\;{2 h c}/{λ_1}-\;{h c}/{λ_2}=\;{h c}/{λ_0}

\;{1}/{λ_0}\;= (\;{2}/{λ_1}-\;{1}/{λ_2})

λ_0\;=\;{λ_1 λ_2}/{2 λ_2-λ_1}

\;\text " Work function "\; ϕ_0\;=\;{h c}/{λ_0}=\;{h c (2 λ_2-λ_1) }/{λ_1 λ_2}

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