The work function of a material is $4.0 \ eV$. The longest wavelength of light that can cause the emission of photoelectrons from this material is approximately ............ $nm$.

The stopping potential $V_0$ for photoelectric emission from a metal surface is plotted along the $Y-$ axis and the frequency $\nu$ of incident light along the $X-$ axis. $A$ straight line is obtained as shown. Planck's constant $h$ is given by:

When photons of energy $1 \ eV$ and $2.5 \ eV$ are incident on a metal surface with a work function of $0.5 \ eV$,what is the ratio of the maximum kinetic energies of the emitted photoelectrons?

$A$ photon of energy $hv$ is absorbed by a free electron of a metal having work function $\phi < hv$.

The maximum velocity of an electron emitted by light of wavelength $\lambda$ incident on the surface of a metal of work function $\phi$ is (Where $h =$ Planck's constant,$m =$ mass of electron,and $c =$ speed of light).

If the wavelengths of incident radiation are $2500 \ \mathring A$ and $5000 \ \mathring A$ respectively,and the work function of the metal surface is $2 \ eV$,find the approximate ratio of the stopping potentials for the emitted photoelectrons. (in $:1$)