If particles move with the same velocity,the de Broglie wavelength is maximum for .........

Find the typical de Broglie wavelength associated with a $He$ atom in helium gas at room temperature $(27^{\circ}C)$ and $1 \; atm$ pressure; and compare it with the mean separation between two atoms under these conditions.

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

Of the following particles having the same kinetic energy,the one which has the largest de Broglie wavelength is

$A$ proton and an electron have the same de Broglie wavelength. If $K_p$ and $K_e$ are the kinetic energies of the proton and electron respectively,then choose the correct relation:

An $\alpha$-particle and a proton are accelerated from rest by a potential difference of $100 \ V$. After this,their de Broglie wavelengths are $\lambda_\alpha$ and $\lambda_{p}$ respectively. The ratio $\frac{\lambda_{p}}{\lambda_\alpha}$,to the nearest integer,is