When a metal plate is illuminated with light of wavelengths $400 \ nm$ and $250 \ nm$,the maximum velocities of the emitted photoelectrons are $v$ and $2v$,respectively. The work function of the metal is ($h$ = Planck's constant; $c$ = speed of light in vacuum):

When light of intensity $1 \ W/m^2$ and wavelength $5 \times 10^{-7} \ m$ is incident on a surface, it is completely absorbed. If $100$ photons emit one electron and the surface area is $1 \ cm^2$, what is the photoelectric current?

$A$ certain metallic surface is illuminated by monochromatic radiation of wavelength $\lambda$. The stopping potential for photoelectric current for this radiation is $3V_{0}$. If the same surface is illuminated with a radiation of wavelength $2\lambda$,the stopping potential is $V_{0}$. The threshold wavelength of this surface for the photoelectric effect is $n\lambda$. Find the value of $n$.

Photons of frequencies equal to the frequencies of $H_\beta$ and $H_{\infty}$ lines of hydrogen are incident on a photosensitive plate,whose threshold frequency is equal to the frequency of the $H_\alpha$ line of hydrogen. The ratio of the maximum kinetic energies of the emitted electrons is

Light strikes a metal surface causing photoelectric emission. The wavelength of incident light is $248 \, nm$. If the stopping potential for the ejected electrons is $2.8 \, eV$, then the work function of the metal is (Take $hc = 1240 \, eV \cdot nm$). (in $ \, eV$)

Photons of wavelength $\lambda$ emitted by a source of power $P$ are incident on a photocell. If the current produced in the cell is $I$,then the percentage of incident photons which produce current in the photocell is: (where $h$ is Planck's constant and $c$ is the speed of light in vacuum)