An electron is accelerated through a potential difference of $10,000 \ V$. Its de-Broglie wavelength is nearly: $(m_{e} = 9 \times 10^{-31} \ kg)$

The kinetic energy of an electron is increased by $2$ times,then the de-Broglie wavelength associated with it changes by a factor.

Assuming the nitrogen molecule is moving with $r.m.s.$ velocity at $400 \ K$, the de$-$Broglie wavelength of the nitrogen molecule is close to $...... \ \mathring{A}$. (Given: nitrogen molecule mass: $4.64 \times 10^{-26} \ kg$, Boltzmann constant: $1.38 \times 10^{-23} \ J/K$, Planck constant: $6.63 \times 10^{-34} \ J \cdot s$)

Which of the following graphs correctly represents the de-Broglie wavelength $\lambda$ associated with a fundamental particle having linear momentum $p$?

The de Broglie wavelength of a proton and $\alpha$-particle are equal. The ratio of their velocities is ...... .

$A$ proton and an $\alpha$-particle are accelerated from rest by $2\,V$ and $4\,V$ potentials, respectively. The ratio of their de-Broglie wavelength is: (in $:1$)