The surface of a metal is illuminated alternately with photons of energies $E_{1} = 4 \ eV$ and $E_{2} = 2.5 \ eV$ respectively. The ratio of maximum speeds of the photoelectrons emitted in the two cases is $2$. The work function of the metal in $eV$ is:

When light of wavelength $\lambda$ is incident on a photosensitive surface,the stopping potential is $V$. When light of wavelength $3 \lambda$ is incident on the same surface,the stopping potential is $\frac{V}{6}$. Then the threshold wavelength for the surface is:

The work functions of Aluminium and Gold are $4.1\,eV$ and $5.1\,eV$ respectively. The ratio of the slope of the stopping potential versus frequency plot for Gold to that of Aluminium is $.......$

Photoelectric effect can be explained by

$A$ silver ball of radius $4.8 \ cm$ is suspended by a thread in a vacuum chamber. $UV$ light of wavelength $200 \ nm$ is incident on the ball for some time,during which a total energy of $1 \times 10^{-7} \ J$ falls on the surface. Assuming that on average one out of $10^3$ incident photons is able to eject an electron,the potential on the sphere will be ............ $V$.

$K_1$ and $K_2$ are the maximum kinetic energies of photoelectrons emitted from a surface of a given material for light of wavelengths $\lambda_1$ and $\lambda_2$, respectively. If $\lambda_1 = 2\lambda_2$, then the work function of the material is given by: