The threshold frequency of metal is f 0 . When the light of frequency 2 f 0 is incident on the metal plate, the maximum velocity of photoelectron is v 1 . When the frequency of incident radiation is i

Question

The threshold frequency of metal is f 0 . When the light of frequency 2 f 0 is incident on the metal plate, the maximum velocity of photoelectron is v 1 . When the frequency of incident radiation is increased to 5 f 0 . the maximum velocity of photoelectrons emitted is v 2 . The ratio of v 1 to v 2 is:

TestHub · Accepted Answer

Maximum kinetic energy is related to the incident frequency $f$ and the threshold frequency $f_{0}$ as:

$K_{\max} = h f - h f_{0}$

When, $f = 2 f_{0}$

$\frac{1}{2} m v_{1}^{2} = 2 h f_{0} - h f_{0} = h f_{0} . . . (1)$

When, $f = 5 f_{0}$

$\frac{1}{2} m v_{2}^{2} = 5 h f_{0} - h f_{0} = 4 h f_{0} . . . (2)$

Hence, the ratio, $\frac{v_{1}}{v_{2}} = \frac{1}{2}$

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