If the kinetic energy of a free electron is doubled,its de Broglie wavelength becomes ........... times.

The de-Broglie wavelength of a neutron at $27^{\circ} C$ is $\lambda_0$. What will be its wavelength at $927^{\circ} C$?

The speed of an electron having a wavelength of $10^{-10} \ m$ is ................. $ \times 10^6 \ m/s$.

An $\alpha$-particle and a proton are accelerated from rest by the same potential,then the ratio of their de-Broglie wavelength is

An $\alpha$ particle and a proton are accelerated from rest by a potential difference of $200 \ V$. After this,their de Broglie wavelengths are $\lambda_{\alpha}$ and $\lambda_{p}$ respectively. The ratio $\frac{\lambda_{p}}{\lambda_{\alpha}}$ is

If a proton is accelerated through a potential difference of $1000 \,V$, then its de-Broglie wavelength is (given, $m_p = 1.67 \times 10^{-27} \,kg$, $h = 6.63 \times 10^{-34} \,J-s$).