$V$ (stopping potential) is plotted against $\frac{1}{\lambda}$,where $\lambda$ is the wavelength of incident radiation,for two metals.

When photons of wavelength $\lambda_1$ are incident on an isolated sphere,the corresponding stopping potential is found to be $V$. When photons of wavelength $\lambda_2$ are used,the corresponding stopping potential is thrice that of the above value. If light of wavelength $\lambda_3$ is used,then find the stopping potential for this case.

In a photoelectric experiment, the wavelength of the light incident on the metal is changed from $200 \, nm$ to $400 \, nm$. The decrease in the stopping potential is close to [Use $hc = 1240 \, eV \cdot nm$ where $h$ is Planck's constant and $c$ is the velocity of light]. (in $ \, V$)

Photoelectric emission takes place from a certain metal at threshold frequency $v$. If the radiation of frequency $4v$ is incident on the metal plate,the maximum velocity of the emitted photoelectrons will be ($m=$ mass of photoelectron,$h=$ Planck's constant).

In the photoelectric effect, an electromagnetic wave is incident on a metal surface and electrons are ejected from the surface. If the work function of the metal is $2.14 \text{ eV}$ and the stopping potential is $2 \text{ V}$, what is the wavelength of the electromagnetic wave (in $\text{ nm}$)? (Given $hc = 1242 \text{ eV nm}$, where $h$ is Planck's constant and $c$ is the speed of light in vacuum.)

The figure represents a graph of the maximum kinetic energy $(K)$ of photoelectrons (in $eV$) versus the frequency $(\nu)$ of incident radiation for a metal used as a cathode in a photoelectric experiment. The work function of the metal is ............. $eV$.