# A metal surface is exposed to

Question:

A metal surface is exposed to $500 \mathrm{~nm}$ radiation. The threshold frequency of the metal for photoelectric current is $4.3 \times 10^{14} \mathrm{~Hz}$. The velocity of ejected electron is $\times 10^{5} \mathrm{~ms}^{-1}$ (Nearest integer)

$\left[\right.$ Use $\left.: \mathrm{h}=6.63 \times 10^{-34} \mathrm{Js}, \mathrm{m}_{\mathrm{e}}=9.0 \times 10^{-31} \mathrm{~kg}\right]$

Solution:

$v:$ speed of electron having max. K.E.

$\Rightarrow$ from Einstein equation : $E=\phi+K \cdot E \cdot \max$

$\Rightarrow \frac{\mathrm{hc}}{\lambda}=\mathrm{hv}_{0}+\frac{1}{2} \mathrm{mv}^{2}$

$\Rightarrow \frac{6.63 \times 10^{-34} \times 3 \times 10^{8}}{500 \times 10^{-9}}=6.63 \times 10^{-34} \times 4.3 \times 10^{14}+\frac{1}{2} \mathrm{mv}^{2}$

$\Rightarrow \frac{6.63 \times 30 \times 10^{-20}}{5}=6.63 \times 4.3 \times 10^{-20}+\frac{1}{2} \mathrm{mv}^{2}$

$\Rightarrow 11.271 \times 10^{-20} \mathrm{~J}=\frac{1}{2} \times 9 \times 10^{-31} \times v^{2}$

$\Rightarrow \mathrm{v}=5 \times 10^{5} \mathrm{~m} / \mathrm{sec}$