Q.

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?

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a

The angular width of the central maximum will decrease.

b

The angular width of the central maximum will be unaffected.

c

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

d

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

answer is A.

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Detailed Solution

de Broglie wavelength of an electronλ=hp=hmvwhere m is the mass and v is the speed of the electron respectively.If speed v of electron is increased, momentum p (= mv) will increase. Hence, wavelength λ will decrease.Angular width of the central maximum is θ0=2λawhere a is the width of slit.If λ  decreases, θ0 will decreaseTherefore, the correct statement is (a).
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