# 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 spec of the electrons is increased, which of the following statements is correct ? Option 1) The angular width of the central maximum will be unaffected. Option 2) Diffraction pattern is not observed on the screen in the case of electrons. Option 3) The angular width of the central maximum of the diffraction pattern will increase. Option 4) The angular width of the central maximum will decrease.

As we learnt in

$R=1.22\frac{\lambda D}{b}$

- wherein

$D=$ Distance of screen from hole

$b=$ slit width

If speed of electron is increased then its wavelength $\lambda = \frac{h}{mv}$

will decrease.

Since angular width $\alpha\:\: \lambda$

hence angular width of central maximum will decrease.

Option 1)

The angular width of the central maximum will be unaffected.

This solution is incorrect.

Option 2)

Diffraction pattern is not observed on the screen in the case of electrons.

This solution is incorrect.

Option 3)

The angular width of the central maximum of the diffraction pattern will increase.

This solution is incorrect.

Option 4)

The angular width of the central maximum will decrease.

This solution is correct.

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