The de Broglie wavelength associated with a proton changes by $0.25\%$. If its momentum changes by $p_0$,then its initial momentum is ......

An $\alpha$-particle and a proton are accelerated from rest by the same potential. The ratio of their de-Broglie wavelengths is . . . . . .

The voltage applied to an electron microscope to produce electrons of wavelength $0.50 \text{ Å}$ is (in $\text{ V}$)

$A$ particle of mass $1 \times 10^{-30} \,kg$ and electric charge $1.6 \times 10^{-19} \,C$ has a de-Broglie wavelength of $660 \,nm$. The kinetic energy of this particle is (Planck's constant,$h = 6.6 \times 10^{-34} \,J \cdot s$)

The ratio of de Broglie wavelengths of a proton and an $\alpha$-particle having the same energy is ............

The wavelength $\lambda$ of a photon and the de-Broglie wavelength of an electron have the same value. The ratio of the kinetic energy of the electron to the energy of a photon is ($m=$ mass of electron,$c=$ velocity of light,$h=$ Planck's constant).