Graph shows the variation of de-Broglie wavelength $\lambda$ versus $\frac{1}{\sqrt{V}}$ where $V$ 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, P, Q, R, S carrying same charge but of mass $m_1, m_2, m_3, m_4$. Which one represents a particle of smaller mass?
$m_4$
$m_1$
$m_3$
$m_2$
Solution
De-broglie wavelength,
$\lambda=\frac{h}{p}$
Kinetic energy :
$\begin{aligned}
& K=\frac{p^2}{2 m}=q V \\
& \lambda=\frac{h}{\sqrt{2 m q V}}
\end{aligned}$
Slope of straight line
$\tan \theta=\frac{h}{\sqrt{2 m q}}$
Hence, more is slope of line, less is the mass.
