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CBSE Class 12 Physics 2015 Delhi Set 1 Paper

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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 λ1\lambda_1 to λ2\lambda_2. Derive the expressions for the threshold wavelength λ0\lambda_0 and work function for the metal surface.
Solution:  
(i) Einstein's Photoelectric equation
(ii) Important features
(iii)Derivation of expressions for λ0\lambda_0 and work function
hv=ϕ0+kmax⁡h v=\phi_0+k_{\max}
or hv=hv0+12mvmax⁡2h_v = h v_0 + \frac{1}{2} m v^2_{\max}
Important features
(i) kmax⁡k_{\max} depends linearly on frequency vv.
(ii) Existence of threshold frequency for the metal surface.
(Any other two correct features.)
hv=ϕ0+kmax⁡h v=\phi_0+k_{\max}
hcλ1=hcλ0+kmax⁡\frac{h c}{\lambda_1} = \frac{h c}{\lambda_0} + k_{\max} ......(i)
hcλ2=hcλ0+2kmax⁡\frac{h c}{\lambda_2} = \frac{h c}{\lambda_0} + 2 k_{\max} ......(ii)
From (i) and (ii)
2hcλ1−hcλ2=hcλ0\frac{2 h c}{\lambda_1} - \frac{h c}{\lambda_2} = \frac{h c}{\lambda_0}
1λ0=(2λ1−1λ2)\frac{1}{\lambda_0} = \left( \frac{2}{\lambda_1} - \frac{1}{\lambda_2} \right)
λ0=λ1λ22λ2−λ1\lambda_0 = \frac{\lambda_1 \lambda_2}{2 \lambda_2 - \lambda_1}
Work functionϕ0=hcλ0=hc(2λ2−λ1)λ1λ2\text{Work function} \phi_0 = \frac{h c}{\lambda_0} = \frac{h c (2 \lambda_2 - \lambda_1)}{\lambda_1 \lambda_2}
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