$A$ particle of charge $q$,mass $m$,and energy $E$ has de-Broglie wavelength $\lambda$. For a particle of charge $2q$,mass $2m$,and energy $2E$,the de-Broglie wavelength is:

$A$ particle of mass $4M$ at rest disintegrates into two particles of mass $M$ and $3M$ respectively,having non-zero velocities. The ratio of the de-Broglie wavelength of the particle of mass $M$ to that of mass $3M$ will be:

The kinetic energy of an electron and a proton is $10^{-32} \ J$. Then the relation between their de-Broglie wavelengths is

$A$ beam of electrons of energy $E$ scatters from a target having atomic spacing of $1 \, Å$. The first maximum intensity occurs at $\theta = 60^{\circ}$. Then $E$ (in $eV$) is: (Planck constant $h = 6.64 \times 10^{-34} \, Js$, $1 \, eV = 1.6 \times 10^{-19} \, J$, electron mass $m = 9.1 \times 10^{-31} \, kg$)

If the de-Broglie wavelength of an electron accelerated by $150 \ V$ is $10^{-10} \ m$,then the de-Broglie wavelength when accelerated by $600 \ V$ will be .......... $\mathring{A}$.

If the momentum of an electron is changed by $P_m$ and the associated de Broglie wavelength changes by $0.50\ \%$, find the initial momentum of the electron. (in $P_m$)