If $m$ is the mass of an electron and $c$ is the speed of light,then the ratio of the wavelength of a photon of energy $E$ to the wavelength of an electron of the same energy is:

Photo cells are used for the:

$A$ 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 $e = 1.6 \times 10^{-19} \, C$.

One day on a spacecraft corresponds to $2$ days on the earth. The speed of the spacecraft relative to the earth is

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: