Rankers Physics

Diffraction: Practice Problem & Solution

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? (2013)
The angular width of the central maximum will be unaffected
Diffraction pattern is not observed on the screen in the case of electrons
The angular width of the central maximum of the diffraction pattern will increase
The angular width of the central maximum will decrease

Short Solution (Best for NEET):

To solve this problem, we apply the core principles of Diffraction. Understanding the underlying formula is key to arriving at the correct answer below:

The de Broglie wavelength of an electron is $\lambda = \frac{h}{mv}$. As the speed $v$ increases, the wavelength $\lambda$ decreases. The angular width of the central maximum is $2\theta = \frac{2\lambda}{a}$. Since $\lambda$ decreases, the angular width will decrease.

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