Question

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

Answer 1

$v:$ speed of electron having max. $K.E$
$\Rightarrow $ from Einstein equation : $E =\phi+ K . E ._ {\max}$
$\Rightarrow \frac{ hc }{\lambda}= h v_{0}+\frac{1}{2} mv ^{2}$
$\Rightarrow \frac{6.63 \times 10^{-34} \times 3 \times 10^{8}}{500 \times 10^{-9}}$
$=6.63 \times 10^{-34} \times 4.3 \times 10^{14}+\frac{1}{2} mv ^{2}$
$\Rightarrow \frac{6.63 \times 30 \times 10^{-20}}{5}$
$=6.63 \times 4.3 \times 10^{-20}+\frac{1}{2} mv ^{2}$
$\Rightarrow 11.271 \times 10^{-20} J$
$ =\frac{1}{2} \times 9 \times 10^{-31} \times v ^{2}$
$\Rightarrow v=5 \times 10^{5}\, m / \sec$