When a metal surface is illuminated by light of wavelengths $400\ nm$ and $250\ nm,$ the maximum velocities of the photoelectrons ejected are $v$ and $2v$ respectively. The work function of the metal is ($h =$ Plank’s constant, $c =$ velocity of light in air)

Question

Dr. Abubacker · Accepted Answer

(a) By using $\frac{hc}{\lambda} = W_{0} + \frac{1}{2}mv^{2}$
$\Rightarrow \frac{hc}{400 	imes 10^{- 9}} = W_{0} + \frac{1}{2}mv^{2}\ \ \ \ldots(i)$
$and\ \frac{hc}{250 	imes 10^{- 9}} = W_{0} + \frac{1}{2}m(2v)^{2}\ \ \ldots(ii)$
On solving (i) and (ii)
$\frac{1}{2}mv^{2} = \frac{hc}{3}\left\lbrack \frac{1}{250 	imes 10^{- 9}} - \frac{1}{400 	imes 10^{- 9}} ightbrack\ \ldots(iii)$
From equation (i) and (iii) $W_{0} = 2hc 	imes 10^{6}J$

Q. When a metal surface is illuminated by light of wavelengths $400\ nm$ and $250\ nm,$ the maximum velocities of the photoelectrons ejected are $v$ and $2v$ respectively. The work function of the metal is ($h =$ Plank’s constant, $c =$ velocity of light in air)

Explanation

Reviewed by Dr. Abubacker

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