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Q.

A surface irradiated with light $λ$ = 480 nm gives out electrons with maximum velocity v m/s, the cut off wavelength being 600 nm. The same surface would release electrons with maximum velocity 2v m/s if it is irradiated by light of wavelength.

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a

325 nm

b

360 nm

c

384 nm

d

300 nm

answer is D.

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Detailed Solution

$\begin{array}{l} E = W + K . E_{\max} \Rightarrow K . E_{\max} = h c [\frac{1}{λ} - \frac{1}{λ_{0}}] = \frac{1}{2} m v^{2} ...... (1) \\ h c [\frac{1}{λ^{1}} - \frac{1}{λ_{0}}] = \frac{1}{2} m {(2 v)}^{2} ............... (2) \\ (1) \div (2) \\ \frac{[\frac{1}{λ} - \frac{1}{λ_{0}}]}{[\frac{1}{λ^{1}} - \frac{1}{λ_{0}}]} = \frac{1}{4} \end{array}$

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