Two streams of photons, possessing energies equal to five and ten times the work function of metal are incident on the metal surface successively. The ratio of the maximum velocities of the photoelectron emitted, in the two cases respectively, will be

We are given two streams of photons with energies $$E_1 = 5\phi$$ and $$E_2 = 10\phi$$, where $$\phi$$ is the work function of the metal.

By the photoelectric equation, the maximum kinetic energy of photoelectrons is $$KE = E - \phi$$.

For the first case: $$\frac{1}{2}mv_1^2 = 5\phi - \phi = 4\phi$$.

For the second case: $$\frac{1}{2}mv_2^2 = 10\phi - \phi = 9\phi$$.

Taking the ratio: $$\frac{v_1^2}{v_2^2} = \frac{4\phi}{9\phi} = \frac{4}{9}$$.

So $$\frac{v_1}{v_2} = \frac{2}{3}$$, i.e., the ratio is $$2:3$$.

Hence, the correct answer is Option C.