Question

Light of wavelength $\lambda$ falls on a metal having work function $hc$ / ${\lambda }_0$. Photoelectric effect will take place only if:

• A. $\lambda \ge {\lambda }_0$
• B. $\lambda \ge 2{\lambda }_0$
• C. $\lambda \le {\lambda }_0$
• D. $\lambda <{\lambda }_0/2$

Answer 1

Answer: (C)

$\lambda \le {\lambda }_0$

$h\nu =h{\nu }_0+K.E$
$\nu \alpha \frac{1}{\lambda }$
$\Rightarrow \frac{hc}{\lambda }=\frac{hc}{{\lambda }_0}+K.E$
$\therefore K.E=\frac{hc}{\lambda {\lambda }_0}({\lambda }_0-\lambda )$
as $K.E\ge 0\Rightarrow {\lambda }_0-\lambda \ge 0\Rightarrow \lambda \le {\lambda }_0$