The graph which shows the variation of $\left(\frac{1}{\lambda^2}\right)$ and its kinetic energy, $E$ is…
The graph which shows the variation of $\left(\frac{1}{\lambda^2}\right)$ and its kinetic energy, $E$ is (where $\lambda$ is de Broglie wavelength of a free particle):
Solution
de-Broglie wavelength $\lambda=\frac{h}{P}=\frac{h}{m v}=\frac{h}{\sqrt{2 m E}}$ where $E=\frac{1}{2} m v^2$
Squaring both sides,
$\begin{aligned}
& \lambda^2=\frac{h^2}{4 m^2 E} \\
& \Rightarrow \frac{1}{\lambda^2}=\text { (constant) } E
\end{aligned}$
Graph passes through origin with constant slope.
