Question

When the light of frequency 2v0​ (where v0​ is threshold frequency), is incident on a metal plate, the maximum velocity of electrons emitted is v1​. When the frequency of the incident radiation is increased to 5v0​, the maximum velocity of electrons emitted from the same plate is v2​. The ratio of v1​ to v2​ is?

Answer 1

Answer:

We know that

$k = e - \phi$

Now in form of frequency , intially

$h \nu_1 = h(2 \nu_0) - h \nu_0 \\ \\ \frac{1}{2} m {v}^{2} = h\nu_0 \\ \\ v_1 = \sqrt{2mh\nu_0}$

Again when

$h \nu_2 = h(5 \nu_0) - h \nu_0 \\ \\ \frac{1}{2} m {v_2}^{2} = 4h\nu_0 \\ \\ v_1 = \sqrt{8mh\nu_0}$

So ratio

$\frac{ v_1}{ v_2} = \frac{ \sqrt{ 2mh \nu_0}}{\sqrt{8mh\nu_0} } = \frac{1}{2}$

So ratio of