The threshold frequency of a metal is ' F 0 '. When light of frequency 2 F 0 is incident on the metal plate, the maximum velocity of photoelectron is ' V 1 ' When the frequen

Question

The threshold frequency of a metal is ' F 0 ​ '. When 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

According to Einstein's photoelectric equation:

$\frac{1}{2} m v^{2} = h f - h F_{0}$

For the first case, $f = 2 F_{0}$ :

$\frac{1}{2} m V_{1}^{2} = h (2 F_{0}) - h F_{0} = h F_{0}$

For the second case, $f = 5 F_{0}$ :

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

Dividing the two equations:

$\frac{V _{1}^{2}}{V _{2}^{2}} = \frac{h F _{0}}{4 h F _{0}} = \frac{1}{4}$

Taking the square root:

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

Answer: $\frac{1}{2}$

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