Ultraviolet radiations of $6.2 \, eV$ fall on an aluminium surface (work function $4.2 \, eV$). The kinetic energy in joules of the fastest electron emitted is approximately:

$A$ metal is exposed to light of wavelength $800 \, nm$ and emits photoelectrons with a certain kinetic energy. The maximum kinetic energy of the photoelectrons doubles when light of wavelength $500 \, nm$ is used. The work function of the metal is $... \, eV$ (Take $hc = 1230 \, eV \cdot nm$).

$A$ 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 ............. $V$.

$A$ metal surface of work function $1.13 eV$ is irradiated with light of wavelength $310 nm$. The retarding potential required to stop the escape of photoelectrons is [Take $hc = 1240 eV \cdot nm$] (in $V$)

For a given surface,the slope of the graph between the frequency of incident light and the stopping potential is .......

Light of energy $E$ falls normally on a metal of work function $\frac{E}{3}$. The kinetic energies $K$ of the photoelectrons are