When a metal surface is illuminated by light of wavelengths $400\; nm$ and $250\; nm$,the maximum velocities of the photoelectrons ejected are $v$ and $2v$ respectively. The work function of the metal is ($h =$ Planck's constant,$c =$ velocity of light in air).

The surface of a certain metal is first illuminated with light of wavelength $\lambda_1 = 350 \ nm$ and then with light of wavelength $\lambda_2 = 540 \ nm$. It is found that the maximum speed of the photoelectrons in the two cases differs by a factor of $2$. The work function of the metal (in $eV$) is close to: (Energy of photon $= \frac{1240}{\lambda \text{ (in } nm)} \ eV$)

When photons of energy $5 eV$ are incident on a metal surface with a work function of $4.36 eV$,photoelectrons are emitted. What is the maximum momentum of the emitted photoelectrons?

Light of wavelength $5000 \; \mathring A$ falls on a sensitive plate with photoelectric work function of $1.9 \; eV$. The kinetic energy of the photoelectron emitted will be ............ $eV$.

When radiation of wavelength $\lambda$ is used to illuminate a metallic surface,the stopping potential is $V.$ When the same surface is illuminated with radiation of wavelength $3 \lambda,$ the stopping potential is $\frac{V}{4}.$ If the threshold wavelength for the metallic surface is $n \lambda,$ then the value of $n$ will be......

An electromagnetic wave of wavelength $\lambda$ is incident on a photosensitive surface of negligible work function. If the photoelectron emitted from the surface has mass $m$ and de-Broglie wavelength $\lambda_{d}$,then