A parallel beam of fast-moving electrons is incident normally on a narrow slit. A diffraction patter

Question

A parallel beam of fast-moving electrons is incident normally on a narrow slit. A diffraction pattern is observed on a screen. If the accelerating voltage applied to the electrons is quadrupled, the angular width of the central maximum will

Professor PC Thomas Classes · Answer

(a) : The de Broglie wavelength of an electron accelerated through a voltage $V$ is $\lambda = \frac{h}{\sqrt{2meV}}$. If $V$ is quadrupled, $\lambda$ becomes halved. The angular width of the central maximum in a single slit diffraction pattern is $2	heta = \frac{2\lambda}{a}$. Since the wavelength $\lambda$ is halved, the angular width of the central maximum also becomes half of its initial value.