Question

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

• A. $\lambda =\left(\frac{2m}{hc}\right){\lambda }_d{}^2$
• B. ${\lambda }_d=\left(\frac{2mc}{h}\right){\lambda }^2$
• C. $\lambda =\left(\frac{2mc}{h}\right){\lambda }_d{}^2$
• D. $\lambda =\left(\frac{2h}{mc}\right){\lambda }_d{}^2$

Answer 1

Answer: (C)

$K_{\text{max }}=\frac{hc}{\lambda }$
$\Rightarrow \frac{p^2}{2m}=\frac{hc}{\lambda }$
$\Rightarrow p=\sqrt{\frac{2mhc}{\lambda }}$
$\Rightarrow {\lambda }_d=\frac{h}{p}=h\sqrt{\frac{\lambda }{2mhc}}=\sqrt{\frac{\lambda h}{2mc}}$
$\Rightarrow \lambda =\left(\frac{2mc}{h}\right){\lambda }_d^2$