The work function of a material is $4.0 \ eV$. The maximum wavelength of light that can cause the emission of photoelectrons from the material is ............ $nm$.

$A$ monochromatic light source of intensity $5 \, mW$ emits $8 \times 10^{15}$ photons per second. This light ejects photoelectrons from a metal surface. The stopping potential for this setup is $2.0 \, V$. The work function of the metal will be ............ $eV$. (in $.9$)

Radiation of wavelength $332 \ nm$ is incident on a metal surface having a work function of $1.07 \ eV$. The stopping potential required to stop the emission of photoelectrons from the metal surface is ............ $V$. $(h = 6.6 \times 10^{-34} \ J s, c = 3 \times 10^8 \ m/s, 1 \ eV = 1.6 \times 10^{-19} \ J)$

The maximum kinetic energy of a photoelectron liberated from the surface of lithium with work function $2.35 \text{ eV}$ by electromagnetic radiation whose electric component varies with time as: $E=a[1+\cos(2 \pi f_1 t)] \cos(2 \pi f_2 t)$ (where $a$ is a constant) is (given $f_1=3.6 \times 10^{15} \text{ Hz}$,$f_2=1.2 \times 10^{15} \text{ Hz}$ and Planck's constant $h=6.6 \times 10^{-34} \text{ Js}$) (in $\text{ eV}$)

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.

Sodium and copper have work functions $2.3 \ eV$ and $4.5 \ eV$ respectively. Then the ratio of their threshold wavelengths is nearest to