The electron in the hydrogen atom jumps from excited state $(n = 3)$ to its ground state $(n = 1)$ and the photons thus emitted irradiate a photosensitive material. If the work function of the material is $5.1 \, eV$,the stopping potential is estimated to be (the energy of the electron in $n^{th}$ state $E_n = \frac{-13.6}{n^2} \, eV$) (in $, V$)

In a photoemissive cell with exciting wavelength $\lambda$,the fastest electron has speed $v$. If the exciting wavelength is changed to $\frac{3\lambda}{4}$,the speed of the fastest emitted electron will be

For the photoelectric effect,which of the following statements are true?
$I$ The kinetic energies of the photoelectrons do not depend on the frequency of light.
$II$ The photoelectric effect will always occur for highly intense light.
$III$ The maximum kinetic energy of a photoelectron does not depend upon the intensity of the light.
$IV$ The escaping electron's kinetic energy is larger for a larger frequency.

Two photons of energy $2.5 eV$ and $3.5 eV$ fall on a metal surface of work function $1.5 eV$. The ratio of the maximum velocities of the photoelectrons emitted from the metal surface is

The work function of metals is in the range of $2 eV$ to $5 eV$. Find which of the following wavelengths of light cannot be used for the photoelectric effect (in $nm$)? (Consider, Planck constant $= 4 \times 10^{-15} eVs$, velocity of light $= 3 \times 10^{8} m/s$)

Einstein's photoelectric equation is given by .........