$A$ photon of wavelength $3315 \ \text{Å}$ falls on a photocathode and an electron of energy $3 \times 10^{-19} \ \text{J}$ is ejected. The threshold wavelength of the photon is [Planck's constant $(h)$ $= 6.63 \times 10^{-34} \ \text{J-s}$, velocity of light $(c)$ $= 3 \times 10^{8} \ \text{m/s}$]. (in $\text{Å}$)

In an experiment on the photoelectric effect,the wavelength of the incident radiation is $\lambda$. The wavelength of the incident radiation is reduced to $\frac{1}{3}$ of the initial value,and the maximum kinetic energy of the photoelectron is observed to be $n$ times the previous value. The threshold wavelength for the metal plate is:

$A$ 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 $eV$.

Initially,a photon of wavelength $\lambda_1$ falls on a photocathode and emits an electron of maximum energy $E_1$. If the wavelength of the incident photon is changed to $\lambda_2$,the maximum energy of the electron emitted becomes $E_2$. Then the value of $hc$ ($h=$ Planck's constant,$c=$ velocity of light) is

$A$ certain metallic surface is illuminated with monochromatic light of wavelength $\lambda$. The stopping potential for the photoelectric current for this light is $3V_0$. If the same surface is illuminated with light of wavelength $2\lambda$,the stopping potential is $V_0$. The threshold wavelength for this surface for the photoelectric effect is:

Two light beams of different frequencies,having energies $1 \ eV$ and $2.5 \ eV$ respectively,are incident on a metal surface with a work function of $0.5 \ eV$. The ratio of the maximum kinetic energies of the emitted photoelectrons is: