$A$ 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 $:1$)

Hydrogen and helium atoms are at temperatures of $27^{\circ}C$ and $127^{\circ}C$ respectively. Find the ratio of their de Broglie wavelengths.

The de Broglie wavelength $\lambda$ associated with a proton increases by $25 \%$,if its momentum is decreased by $p_0$. The initial momentum was

If a ball of mass $1 \ kg$ has a velocity of $1 \ m/s$,what is its de Broglie wavelength?

$A$ proton and an electron are associated with the same de-Broglie wavelength. The ratio of their kinetic energies is:
(Assume $h=6.63 \times 10^{-34} \ J \ s$,$m_{e}=9.0 \times 10^{-31} \ kg$ and $m_{p}=1836 \times m_{e}$)

The de Broglie wavelength of an oxygen molecule at $27^{\circ} C$ is $x \times 10^{-12} \ m$. The value of $x$ is (take Planck's constant $= 6.63 \times 10^{-34} \ J \cdot s$,Boltzmann constant $= 1.38 \times 10^{-23} \ J/K$,mass of oxygen molecule $= 5.31 \times 10^{-26} \ kg$).