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

$A$ particle $A$ of mass $m$ and charge $q$ is accelerated by a potential difference of $50 \ V$. Another particle $B$ of mass $4m$ and charge $q$ is accelerated by a potential difference of $2500 \ V$. The ratio of de-Broglie wavelength $\frac{\lambda_A}{\lambda_B}$ is close to

If a proton and an alpha particle are accelerated through the same potential difference, then the ratio of their de Broglie wavelengths is

The graph shows the variation of de-Broglie wavelength $\lambda$ versus $\frac{1}{\sqrt{V}}$,where $V$ is the accelerating potential for four particles carrying the same charge but having masses $m_1, m_2, m_3, m_4$. Which one represents the particle with the smallest mass?

An electron with an initial kinetic energy of $100 \, eV$ is accelerated through a potential difference of $50 \, V$. The final de-Broglie wavelength of the electron becomes .................... $\mathring{A}$

State the de-Broglie hypothesis.