$A$ photocell is illuminated by a $100 \ W$ mercury source. It emits ultraviolet light of wavelength $2271 \ \mathring A$. If the stopping potential is $1.3 \ V$,find the work function of the metal in $eV$.

When a metallic surface is illuminated with radiation of wavelength $\lambda$,the stopping potential is $V$. If the same surface is illuminated with radiation of wavelength $2\lambda$,the stopping potential is $\frac{V}{4}$. The threshold wavelength for the metallic surface is:

Two streams of photons,possessing energies equal to twice and ten times the work function of a metal,are incident on the metal surface successively. The ratio of the maximum velocities of the photoelectrons emitted in the two respective cases is $x:y$. The value of $x$ is ...... .

Given below are two statements:
Statement $I$: Stopping potential in photoelectric effect does not depend on the power of the light source.
Statement $II$: For a given metal,the maximum kinetic energy of the photoelectron depends on the wavelength of the incident light.
In the light of the above statements,choose the most appropriate answer from the options given below.

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):

$A$ metal surface is illuminated by light of two different wavelengths $248 \ nm$ and $310 \ nm$. The maximum speeds of the photoelectrons corresponding to these wavelengths are $u_1$ and $u_2$,respectively. If the ratio $u_1: u_2 = 2: 1$ and $hc = 1240 \ eV \ nm$,the work function of the metal is nearly: (in $eV$)