Single Choice

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 statement is correct?

ADiffraction pattern is not observed on the screen in the case of electrons
BThe angular width of the central maximum of the diffraction pattern will increase
CThe angular width of the central maximum will decreases
Correct Answer
DThe angular width of the central maximum will remain unaffected

Solution

We know that $$\lambda=\dfrac{h}{mv}$$
Also for angular width
$$\omega=\dfrac{2\lambda}{d}$$
So we can say $$\omega\propto\lambda\propto \dfrac{1}{v}$$
So if the velocity increases, the angular width of the central maximum will decrease.

SIMILAR QUESTIONS

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For Bragg's diffraction by a crystal to occur, then which of the following is correct for the X-ray of wavelength $$\lambda$$ and interatomic distance d :

Wave Optics

A plane monochromatic wave of natural light with intensity $$I_0$$ falls normally on a screen composed of two touching Polaroid half-planes. The principal direction of one Polaroid is parallel and that of the other between them. What kind of diffraction pattern is formed behind the screen? What is the intensity of light behind the screen at the points of the plane perpendicular to the screen and passing through the boundary between the Polaroids?

Wave Optics

A light with wavelength $$\lambda = 0.60 \mu m$$ falls normally on a diffraction grating inscribed on a plane surface of a plano-convex cylindrical glass lens with curvature radius $$R = 20 cm$$. the period of grating is equal to $$d = 6.0 \mu m$$. Find the distance between the principal maxima of first order located symmetrically in the focal plane of that lens.

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Light with wavelength $$\lambda$$ falls on a diffraction grating at right angles. Find the angular dispersion of grating as a function of diffraction angle $$\theta$$.

Wave Optics

As a result of interference of two coherent sources of light, energy is:

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