An electromagnetic wave of wavelength ' $λ$ ' is incident on a photosensitive surface of negligible work function. If 'm' mass is of photoelectron emitted from the surface has de-Broglie wavelength d $λ$ _d, then :

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$λ = (\frac{2 m}{hc}) λ_{d}^{2}$

$λ = (\frac{2 h}{mc}) λ_{d}^{2}$

$λ = (\frac{2 mc}{h}) λ_{d}^{2}$

$λ_{d} = (\frac{2 mc}{h}) λ^{2}$

answer is D.

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Detailed Solution

$\begin{array}{l} K_{max} = \frac{hc}{λ} \\ \Rightarrow \frac{p^{2}}{2 m} = \frac{hc}{λ} \Rightarrow p = \sqrt{\frac{2 mhc}{λ}} \\ \Rightarrow λ_{d} = \frac{h}{p} = h \sqrt{\frac{λ}{2 mhc}} = \sqrt{\frac{λh}{2 mc}} \Rightarrow λ = (\frac{2 mc}{h}) λ_{d}^{2} \end{array}$