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?
The angular width of the central maximum of the diffraction pattern will increase.
The angular width of the central maximum will decrease.
The angular width of the central maximum will be unaffected.
A diffraction pattern is not observed on the screen in the case of electrons.
According to de Broglie's hypothesis, the wavelength of an electron is inversely proportional to its momentum (and hence speed), given by . When the speed () of the electrons is increased, their de Broglie wavelength () decreases. The angular width of the central maximum in a single slit diffraction pattern is directly proportional to the wavelength, given by , where is the slit width. Therefore, a decrease in wavelength results in a decrease in the angular width of the central maximum.
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