Question

A parallel beam of fast moving electrons is incident normally on a narrow slit. A fluorescent screen is placed at a large distance from the slit. If the speed of the electrons is increased, which of the following statements is correct?

• A. The angular width of the central maximum will be unaffected
• B. Diffraction pattern is not observed on the screen in the case of electrons.
• C. The angular width of the central maximum will increase
• D. The angular width of the central maximum will decrease

Answer 1

The correct option is D The angular width of the central maximum will decrease

According to de-Broglie's hypothesis,
$\lambda =\frac{h}{p}=\frac{h}{mv}$

$\Rightarrow \lambda \propto \frac{1}{v}\dots \left(1\right)$

Angular width of the central maxima is $w=\frac{2\lambda D}{a}$
$\Rightarrow w\propto \lambda \dots \left(2\right)$

From $\left(1\right)$ and $\left(2\right)$, we can write,

$w\propto \frac{1}{v}$

So, as the speed of electron increases, the wavelength of electrons will decrease and hence the angular width of the central maximum of the diffraction pattern will decrease.

<!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> Hence, $\left(D\right)$ is the correct answer.