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Q.

if $λ_{o}$ is the threshold wavelength for photoelectric emission, $λ$ the wavelength of light falling on the surface of a metal and ‘m’ is the mass of the electron, then the velocity of ejected electron is given by

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a

${[\frac{2 h}{m} (λ_{o} - λ)]}^{1 / 2}$

b

${[\frac{2 hc}{m} (λ_{o} - λ)]}^{1 / 2}$

c

${[\frac{2 hc}{m} (\frac{λ_{o} - λ}{λ_{o} λ})]}^{1 / 2}$

d

${[\frac{2 h}{m} (\frac{1}{λ_{o}} - \frac{1}{λ})]}^{1 / 2}$

answer is C.

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Detailed Solution

$hν = {hν}_{o} + K . E \frac{hc}{λ} = \frac{hc}{λ_{o}} + \frac{1}{2} {mv}^{2}$

$v = {[\frac{2 hc}{m} (\frac{λ_{o} - λ}{λ_{o} λ})]}^{1 / 2}$

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if λo is the threshold wavelength for photoelectric emission, λ the wavelength of light falling on the surface of a metal and ‘m’ is the mass of the electron, then the velocity of ejected electron is given by