When a metal surface is illuminated by light of wavelengths 400 nm and 250 nm, the maximum velocities of the photoelectlons ejected are v and 2v respectively. The work function of the metal is (h : Planck's constant, c : velocity of light in air)

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$2 hc \times 10^{6} J$

$1.5 hc \times 10^{6} J$

$hc \times 10^{6} J$

$0.5 hc \times 10^{6} J$

answer is A.

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Detailed Solution

$\begin{array}{l} By using \frac{hc}{λ} = W_{o} + \frac{1}{2} {mv}^{2} \\ \Rightarrow \frac{hc}{400 \times 10^{- 9}} = W_{o} + \frac{1}{2} {mv}^{2} . . . . (i) \\ and \frac{hc}{250 \times 10^{- 9}} = W_{o} + \frac{1}{2} m {(2 v)}^{2} . . (ii) \\ on solving (i) and (ii) \\ \frac{1}{2} {mv}^{2} - \frac{hc}{3} [\frac{1}{250 \times 10^{- 9}} - \frac{1}{400 \times 10^{- 9}}] . (iii) \\ From equation (i) and (iii), W_{o} = 2 hc \times 10^{6} J . \end{array}$