When photons of energies twice and thrice the work function of a metal are incident on the metal surface one after other, the maximum velocities of the photoelectrons emitted in the two cases are $V_1$ and $V_2$ respectively. The ratio $\mathrm{V}_1: \mathrm{V}_2$ is

When a light of wavelength $\lambda$ falls on the emitter of a photocell, maximum speed of emitted photoelectrons is V . If the incident wavelength is changed to $\frac{2 \lambda}{3}$, maximum speed of emitted photoelectrons will be :

The de-Broglie wavelength $(\lambda)$ of a particle

Photoelectric emission is observed from a metallic surface for frequencies $v_1$ and $v_2$ of the incident light rays $\left(v_1>v_2\right)$. If the maximum values of kinetic energy of the photoelectrons emitted in the two cases are in the ratio of $1: \mathrm{k}$, then the threshold frequency of metallic surface is