The de Broglie wavelength of a particle moving with a speed of $0.8 c$ is equal to the wavelength of a photon. If $c$ is the speed of light in vacuum, the ratio of the energy of the photon to the kinetic energy of the particle is:

The dual nature of radiation is demonstrated by:

$A$ light beam of wavelength $500 \, nm$ is incident on a metal having a work function of $1.25 \, eV$,placed in a magnetic field of intensity $B$. The electrons emitted perpendicular to the magnetic field $B$,with maximum kinetic energy,are bent into a circular arc of radius $30 \, cm$. The value of $B$ is $.... \times 10^{-7} \, T$.
Given $hc = 20 \times 10^{-26} \, J \cdot m$,mass of electron $m_e = 9 \times 10^{-31} \, kg$,and $e = 1.6 \times 10^{-19} \, C$.

In a photoelectric experiment,light of wavelength $800 \ nm$ produces photoelectrons with the smallest de Broglie wavelength of $1 \ nm$. Then the work function of the metal used in the experiment is nearly (in $eV$)

For a body moving with relativistic speed,if the velocity is doubled,then

Find the number of photons emitted per second from a source of light which results in a photocurrent with drift velocity of $1.5 \ m/s$ in a conductor with cross-section area $0.25 \ m^2$ and volume density of electrons $10^{20} \ m^{-3}$. (Assume that $60\%$ of photons emitted result in electron emission).