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Q.

The de Broglie wavelength ( $λ$ ) associated with a photoelectron varies with the frequency (v) of the incident radiation as, [v₀ is threshold freqency]

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a

\lambda \propto \frac{1}{{{(v-{{v}_{0}})}^{\frac{1}{4}}}}\

b

\lambda \propto \frac{1}{{{(v-{{v}_{0}})}^{\frac{3}{2}}}}\

c

\lambda \propto \frac{1}{(v-{{v}_{0}})}\

d

\lambda \propto \frac{1}{{{(v-{{v}_{0}})}^{\frac{1}{2}}}}\

answer is B.

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Detailed Solution

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KE of photoelectrons
KE $=h\upsilon -h{{\upsilon }_{0}}\$ ... (1)

$\lambda =\frac{h}{\sqrt{2mKE}}\$ ... (2)

substituting 1 in 2

$\lambda ={\frac{h}{\sqrt 2mh\left( v-{{v}_{0}} \right)}}$ ( $\therefore \$ h, m are constants)

$\Rightarrow \lambda \propto \frac{1}{{{\left( v-{{v}_{0}} \right)}^{\frac{1}{2}}}}$

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