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 radiatio

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 v 1 ​ to v 2 ​ is

TestHub · Accepted Answer

Using Einstein's photoelectric equation:

$K_{m a x} = h f - h f_{0}$

For incident frequency $2 f_{0}$ :

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

For incident frequency $5 f_{0}$ :

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

Taking the ratio of the two equations:

$\frac{v _{1}^{2}}{v _{2}^{2}} = \frac{h f _{0}}{4 h f _{0}} = \frac{1}{4}$

$\frac{v _{1}}{v _{2}} = \frac{1}{2}$

Answer: $1 : 2$

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