An electron of mass $m$ and a photon have the same energy $E$. The ratio of the de-Broglie wavelengths associated with them is:

An $\alpha$-particle moves in a circular path of radius $0.83\, cm$ in the presence of a magnetic field of $0.25\, Wb/m^2$. The de Broglie wavelength associated with the particle will be .............. $\mathring{A}$.

The idea of matter waves was given by

The velocity of a particle $A$ is $3$ times the velocity of a proton. If the ratio of the de Broglie wavelengths of the particle $A$ and the proton is $3:2$,the mass of the particle $A$ is (where $m_{p}$ is the mass of the proton).

$A$ particle of mass $9.1 \times 10^{-31} \, \text{kg}$ travels in a medium with a speed of $10^{6} \, \text{m/s}$ and a photon of radiation with linear momentum $10^{-27} \, \text{kg} \cdot \text{m/s}$ travels in vacuum. The wavelength of the photon is $....$ times the wavelength of the particle.

The de Broglie wavelength of an electron moving with a velocity $1.5 \times 10^8 \, m/s$ is equal to that of a photon. The ratio of the kinetic energy of the electron to the energy of the photon is