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

Concept:

The phenomenon of ejection of electrons from metal surface when a light of frequency greater than the threshold frequency of it is incident on it is known as photoelectric effect.

Energy of incident photon is used to provide threshold energy to the electrons on the metal surface and the energy left is imparted to electron as its kinetic energy.

Equation connecting energy of incident photon and threshold energy and kinetic energy of ejected electron is 

\(E'=E_T+E_e\)

\(hv=hv_0+\frac{1}{2}{\rm mv}^2\)

Frequency of incident photon and threshold frequency of metal surface is v and v0 respectively.

Calculation:

Given-

Threshold frequency = v0

Frequency of incident light = 2v0 

\(h\left( {2{\nu _0}} \right) = h{\nu _0} + \frac{1}{2}mv_1^2\)

\(h{\nu _0} = \frac{1}{2}mv_1^2\)      ----(i)           

\(4h{\nu_0} = \frac{1}{2}mv_2^2\)      ----(ii)           

Divide (i) by (ii),

\(\frac{1}{4} = \frac{{v_1^2}}{{v_2^2}}\)

\(\frac{{{v_1}}}{{{v_2}}} = \frac{1}{2}\)