Question

A metal surface is exposed to $500nm$ radiation. The threshold frequency of the metal for photoelectric current is $4.3\times 10^{14}Hz$. The velocity of ejected electron is ___ $\times 10^{5}m{s}^{-1}$ (Nearest integer)
$[$ Use $:h=6.63\times 10^{-34}Js,m_e=9.0\times 10^{-31}kg]$

Answer 1

Answer: 5

$v:$ speed of electron having max. $K.E$
$\Rightarrow$ from Einstein equation : $E=\varphi +K.E{.}_{\max }$
$\Rightarrow \frac{hc}{\lambda }=h{v}_0+\frac{1}{2}m{v}^2$
$\Rightarrow \frac{6.63\times 10^{-34}\times 3\times 10^8}{500\times 10^{-9}}$
$=6.63\times 10^{-34}\times 4.3\times 10^{14}+\frac{1}{2}m{v}^2$
$\Rightarrow \frac{6.63\times 30\times 10^{-20}}{5}$
$=6.63\times 4.3\times 10^{-20}+\frac{1}{2}m{v}^2$
$\Rightarrow 11.271\times 10^{-20}J$
$=\frac{1}{2}\times 9\times 10^{-31}\times v^2$
$\Rightarrow v=5\times 10^{5}m/\sec$