Question

A photosensitive metallic surface has work function, $h{v}_0$ . If photons of energy $2h{v}_0$ fall on this surface, the electrons come, out with a maximum velocity $4\times {10}^{6}m/s$ . When the photon energy is increased to $5h{v}_0$ , then maximum velocity of photo electrons will be :-

• A. $2\times {10}^{7}m/s$
• B. $2\times {10}^{7}m/s$
• C. $8\times {10}^{5}m/s$
• D. $8\times {10}^{6}m/s$

Answer 1

The correct option is D $8\times {10}^{6}m/s$

From $E=W_0+\frac{1}{2}m{v}_{max}^2$
$\Rightarrow 2h{v}_0=h{v}_0+\frac{1}{2}m{v}_1^2\Rightarrow h{v}_0=\frac{1}{2}m{v}_1^2$
and $5h{v}_0=h{v}_0+\frac{1}{2}m{v}_2^2\Rightarrow 4h{v}_0=\frac{1}{2}m{v}_2^2$
Dividing equation (ii) by (i) $\left(\frac{v_2}{v_1}\right)=\frac{4}{1}$
$\Rightarrow v_2=2v_1=2\times 4\times {10}^6=8\times {10}^{6}m/s$