If a change in the momentum of an electron by $P_o$ results in a change of $0.25\%$ in its de-Broglie wavelength,then the initial momentum is:

If a proton and an electron have the same linear momentum,then compared to the electron:

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

The ratio of de-Broglie wavelength of an $\alpha$-particle and a proton accelerated from rest by the same potential is $\frac{1}{\sqrt{m}}$. The value of $m$ is

The temperature of an ideal gas in $3$-dimensions is $300\, K$. The corresponding de-Broglie wavelength of the electron approximately at $300\, K$ is $....\, nm$.
$[m_e = \text{mass of electron} = 9 \times 10^{-31}\, kg, h = \text{Planck constant} = 6.6 \times 10^{-34}\, Js, k_B = \text{Boltzmann constant} = 1.38 \times 10^{-23}\, JK^{-1}]$

If the de Broglie wavelengths associated with a proton and an $\alpha$-particle are equal,then the ratio of velocities of the proton and the $\alpha$-particle will be