When a metallic surface is illuminated with a radiation of wavelength $\lambda$, the stopping potential is $V$. If the same surface is illuminated with radiation of wavelength $6\lambda$, the stopping potential is $V/12$. The threshold wavelength for the surface is

In the photoelectric effect,the threshold wavelength of sodium is $5000 \ \mathring A$. Find its work function in $eV$. $(h = 6.6 \times 10^{-34} \ J \cdot s, c = 3 \times 10^8 \ m/s, 1 \ eV = 1.6 \times 10^{-19} \ J)$

$A$ zinc ball of radius $1 \,cm$ is charged to a potential of $-0.5 \,V$. The ball is illuminated by a monochromatic ultraviolet light with a wavelength of $290 \,nm$. The photoelectric threshold for zinc is $332 \,nm$. The potential of the ball after a prolonged exposure to the ultraviolet light is ............. $V$.

Two identical photocathodes receive light of frequencies $n_1$ and $n_2$. If the velocities of the emitted photoelectrons of mass $m$ are $V_1$ and $V_2$ respectively, then ($h$ = Planck's constant)

The stopping potential in the context of the photoelectric effect depends on the following property of incident electromagnetic radiation:

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