ISRO Scientific Assistant Physics Question Paper

Explanation:

The question asks how to determine the distance between crystal planes when electrons, accelerated through a given potential difference, produce a first-order Diffraction maximum at a specific glancing angle.

In quantum mechanics, electrons behave as waves when moving with high velocity. This wave nature is described by the de Broglie relation, which links the wavelength of a particle to its momentum. When electrons are accelerated through a potential difference, their kinetic energy increases and their wavelength can be calculated. When these electron waves interact with a crystal, they undergo Diffraction similar to X-rays. The condition for Diffraction maxima in crystals is given by Bragg’s law.

First, the wavelength of the electrons is determined using the de Broglie relation for particles accelerated through a potential difference. Once the wavelength is known, Bragg’s law is applied, which states that constructive interference occurs when 2d sinθ equals an integer multiple of the wavelength. In this situation, the first-order maximum means the order number is one. The given glancing angle represents the angle between the incident beam and the crystal plane. Substituting the wavelength and angle into Bragg’s relation allows calculation of the spacing between adjacent crystal planes.

A similar principle is used in X-ray crystallography where wave interference patterns help determine atomic spacing inside crystals.

Thus, by combining the de Broglie wavelength of electrons with Bragg’s Diffraction condition, the interplanar spacing of the crystal can be determined.

Explanation:

This question asks how to determine the possible distances between parallel crystal planes when X-rays of a known wavelength produce reflection at a specific glancing angle.

X-ray Diffraction occurs when X-rays interact with regularly spaced atoms in a crystal. The crystal acts like a three-dimensional Diffraction grating. The condition for constructive interference between reflected waves is described by Bragg’s law, which states that 2d sinθ equals an integer multiple of the wavelength. Here, d represents the spacing between crystal planes, θ is the glancing angle, and the integer corresponds to the Diffraction order.

In this problem, the wavelength of the incident X-rays and the glancing angle are known. The equation allows multiple solutions because Diffraction can occur for different orders (first, second, third, etc.). Each order corresponds to a different integer value. By substituting the wavelength and angle into Bragg’s law and considering different integer values, different possible values of interplanar spacing can be calculated.

This situation is common in crystallography because several Diffraction orders may satisfy the interference condition for the same angle.

Therefore, by applying Bragg’s law with different diffraction orders, one can determine multiple possible values of the spacing between reflecting crystal planes.

Explanation:

The question asks how to determine the spacing between parallel planes of a crystal when X-rays of a known wavelength produce a first-order diffraction maximum at a given angle in a Bragg crystal spectrometer.

X-ray diffraction occurs when X-ray waves interact with atoms arranged in regularly spaced planes inside a crystal. Because the spacing between these planes is comparable to the wavelength of X-rays, the waves reflected from different planes can interfere constructively or destructively. The condition for constructive interference is given by Bragg’s law, expressed as 2d sinθ = nλ, where d is the spacing between crystal planes, θ is the glancing angle, λ is the wavelength of the X-rays, and n is the diffraction order.

In this problem, the wavelength of the incident X-rays and the diffraction angle are given, along with the information that the diffraction occurs in the first order. First-order diffraction means the integer n equals one. By substituting the known values of wavelength and angle into Bragg’s law, the equation can be rearranged to determine the value of d, which represents the interplanar spacing of the crystal.

Bragg’s spectrometer works on this exact principle and is widely used to determine atomic spacing in crystals.

Thus, using the diffraction condition described by Bragg’s law, the spacing between crystal planes can be determined from the wavelength of the X-rays and the measured diffraction angle.