Question

The maximum velocity of an electron emitted by light of wavelength $\lambda$ incident on the surface of a metal of work-function $\varphi$ is :

• A. $\sqrt{\frac{2(hc+\lambda \varphi )}{m\lambda }}$
• B. $\frac{2(hc+\lambda \varphi )}{m\lambda }$
• C. $\sqrt{\frac{2(hc-\lambda \varphi )}{m\lambda }}$
• D. $\sqrt{\frac{2(h\lambda -\varphi )}{m}}$

Answer 1

Answer: (C)

$\sqrt{\frac{2(hc-\lambda \varphi )}{m\lambda }}$

$K.E{.}_{max}=hv-\varphi$

$\frac{1}{2}m{v}^2=\frac{hc}{\lambda }-\varphi$

$\Rightarrow v=\sqrt{\frac{2(hc-\lambda \varphi )}{m\lambda }}$