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Q.

Radiation of wavelength $λ$ , is incident on a photocell. The fastest emitted electron has speed $v$ . If the wavelength is changed to $\frac{3 λ}{4},$ the speed of the fastest emitted electron will be:

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a

$> v {(\frac{4}{3})}^{\frac{1}{2}}$

b

$= v {(\frac{4}{3})}^{\frac{1}{2}}$

c

$= v {(\frac{3}{4})}^{\frac{1}{2}}$

d

$< v {(\frac{4}{3})}^{\frac{1}{2}}$

answer is C.

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Detailed Solution

$h \frac{c}{λ} - h v_{0} = \frac{1}{2} m v^{2} ∴ \frac{4}{3} \frac{h c}{λ} - h v_{0} = \frac{1}{2} m v'^{2} ∴ \frac{v'^{2}}{v^{2}} = \frac{\frac{4}{3} v - v_{0}}{v - v_{0}} ∴ v' = v \sqrt{\frac{\frac{4}{3} v - v_{0}}{v - v_{0}}} ∴ v' > v \sqrt{\frac{4}{3}}$

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Radiation of wavelength λ , is incident on a photocell. The fastest emitted electron has speed v . If the wavelength is changed to 3λ4, the speed of the fastest emitted electron will be: