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 of $4\times {10}^{6}m/s$. When the photon energy is increases to $5h{v}_0$ then maximum velocity of photo electron will be

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

Answer 1

Answer: (D)

$8\times {10}^{6}m/s$

When photons of frequency, $2{\nu }_0$ are incident then the Einstein equation is $\frac{m{v}_1^2}{2}=2h{\nu }_0-h{\nu }_0$

or $\frac{m{v}_1^2}{2}=h{\nu }_0$ ...........(1)

When $5{\nu }_0$ is incident the Einstein equation becomes

$\frac{m{V}_2^2}{2}=5h{\nu }_0-h{\nu }_0=4h{\nu }_0$ .......(2)

Dividing equation-2 by equation-1 we get $v_2^2=4v_1^2$ or $v_2=2v_1=2\times 4\times {10}^{6}m/s=8\times {10}^{6}m/s$

Option D is correct.