MPSC 2024 Prelims Q56: Which of the following wavelengths are used to study the

Q: What is the answer to MPSC 2024 Prelims Q56?

(3). Correct — option (3), X-Rays wavelength. Studying a crystal's structure means finding how its atoms are arranged in space, and the only way to see an arrangement that fine is to diffract a wave off it. Diffraction is useful only when the wavelength is comparable to the spacing of the obstacles doing the diffracting: much longer and the wave simply passes over the structure without being resolved, much shorter and the diffracted beams crowd so close to the straight-through direction that nothing can be distinguished. The atoms in a crystal are spaced about a tenth of a nanometre apart — one to three angstroms — and X-rays have wavelengths of just that order, roughly 0.01 to 10 nanometres. That coincidence is what makes crystallography possible. The planes of atoms in a crystal act as a natural three-dimensional diffraction grating, and the condition for constructive interference is Bragg's law, which says that twice the spacing between planes multiplied by the sine of the glancing angle equals a whole number of wavelengths. Measuring the angles at which the diffracted beams appear therefore gives the spacings directly, and the pattern of their intensities gives the arrangement of the atoms within the repeating unit. The technique was established when Max von Laue demonstrated the diffraction of X-rays by a crystal in 1912, and William Henry Bragg and William Lawrence Bragg turned it into a method for determining structures. It is the same method that produced the X-ray diffraction photographs of DNA from which the double helix was deduced.

MPSC 2024 Prelims Paper-I · Question 56 of 100

Maharashtra Gazetted Civil Services Combined Preliminary Examination 2024, held 1 December 2024. Transcribed from the commission's own booklet (संच A); answer as per the official MPSC final answer key.

Which of the following wavelengths are used to study the crystal structure of material ?

(1)Ultraviolet wavelength
(2)Gamma Rays wavelength
(3)X-Rays wavelength
(4)Infrared wavelength

Answer

(3)

Why

Correct — option (3), X-Rays wavelength. Studying a crystal's structure means finding how its atoms are arranged in space, and the only way to see an arrangement that fine is to diffract a wave off it. Diffraction is useful only when the wavelength is comparable to the spacing of the obstacles doing the diffracting: much longer and the wave simply passes over the structure without being resolved, much shorter and the diffracted beams crowd so close to the straight-through direction that nothing can be distinguished. The atoms in a crystal are spaced about a tenth of a nanometre apart — one to three angstroms — and X-rays have wavelengths of just that order, roughly 0.01 to 10 nanometres. That coincidence is what makes crystallography possible. The planes of atoms in a crystal act as a natural three-dimensional diffraction grating, and the condition for constructive interference is Bragg's law, which says that twice the spacing between planes multiplied by the sine of the glancing angle equals a whole number of wavelengths. Measuring the angles at which the diffracted beams appear therefore gives the spacings directly, and the pattern of their intensities gives the arrangement of the atoms within the repeating unit. The technique was established when Max von Laue demonstrated the diffraction of X-rays by a crystal in 1912, and William Henry Bragg and William Lawrence Bragg turned it into a method for determining structures. It is the same method that produced the X-ray diffraction photographs of DNA from which the double helix was deduced.

Why the others are wrong

(1)Ultraviolet wavelength — Ultraviolet wavelengths run from about 10 to 400 nanometres, which is between a hundred and several thousand times the distance between neighbouring atoms in a crystal. A wave that long cannot resolve a structure that fine — it is like trying to trace the grain of a wooden plank with a broom handle. Ultraviolet radiation is genuinely useful in the study of matter, but for a different purpose: it excites electronic transitions in atoms and molecules, so ultraviolet and visible spectroscopy reports on energy levels and on the presence of particular chemical groups rather than on the geometry of a lattice.
(2)Gamma Rays wavelength — Gamma rays fail from the opposite direction: their wavelengths are far shorter than the spacing between atomic planes, so the diffraction angles they produce are vanishingly small and the pattern collapses into the undeviated beam. They are also produced by transitions within the nucleus and interact strongly with nuclei rather than with the electron clouds that scatter X-rays, and they are difficult to produce as a monochromatic, well-collimated laboratory beam. Being more energetic does not make a probe better; it makes it the wrong length for this particular measurement.
(4)Infrared wavelength — Infrared wavelengths, from about 700 nanometres upward, are longer still than ultraviolet and therefore even further from the scale of a crystal lattice. Infrared radiation has a well-known analytical use, but it is chemical rather than structural: its energies match the vibrational and rotational transitions of molecules, so infrared spectroscopy identifies the bonds and functional groups present in a substance. It reports what a molecule is made of, not how its atoms are stacked in a solid.

Concept

A crystal is matter in which atoms, ions or molecules are arranged in a pattern that repeats regularly in three dimensions, and determining that pattern is the central problem of solid-state science. Because the repeat distances are of the order of a tenth of a nanometre, no optical microscope can resolve them; the resolution of any imaging or diffraction technique is limited by the wavelength of the probe it uses. X-rays fall in precisely the right range, and a crystal presented to a monochromatic X-ray beam behaves as a three-dimensional grating whose planes reflect the beam only at angles satisfying Bragg's condition, twice the interplanar spacing times the sine of the glancing angle equal to a whole number of wavelengths. From the resulting pattern of spots or rings the lattice parameters and the positions of atoms in the repeating unit can be reconstructed. The same logic supports two related techniques that exploit the wave nature of matter rather than of light: electron diffraction, useful for surfaces and thin films because electrons penetrate very little, and neutron diffraction, which is uniquely good at locating light atoms such as hydrogen and at revealing magnetic ordering, because neutrons scatter from nuclei and from magnetic moments rather than from electron clouds.

MPSC's science and technology questions favour the idea that a measuring technique must be matched to the scale of the thing measured, and this item is the cleanest example of it. A candidate who cannot recall which radiation is used for crystallography can still reason it out from the electromagnetic spectrum: rank the four options by wavelength, note that atomic spacings are of the order of a tenth of a nanometre, and pick the band that sits closest to it. That reasoning generalises across the syllabus — ultraviolet and visible light for electronic transitions and for sterilisation, infrared for molecular vibrations and for thermal imaging, microwaves for rotational transitions and for radar, gamma rays for nuclear processes and for radiotherapy. Learning the spectrum as a ladder of wavelengths with a use attached to each rung answers a whole family of questions rather than one.

Key facts

X-ray wavelengths, of the order of 0.01 to 10 nanometres, are comparable to the spacing between atomic planes in a crystal, which is what makes a crystal act as a natural three-dimensional diffraction grating for them.
Bragg's law states that constructive interference occurs when twice the interplanar spacing multiplied by the sine of the glancing angle equals a whole number of wavelengths, and it converts measured diffraction angles into lattice spacings.
Max von Laue demonstrated the diffraction of X-rays by crystals in 1912, and William Henry Bragg and William Lawrence Bragg developed it into the method of X-ray crystallography for determining atomic structures.
Ultraviolet and visible radiation probe electronic transitions and infrared radiation probes molecular vibrations, so both are chemical rather than structural tools and neither can resolve a lattice.
Electron diffraction and neutron diffraction complement X-ray methods, electrons being suited to surfaces and thin films and neutrons to locating light atoms such as hydrogen and to studying magnetic ordering.

A wave resolves a structure only when its wavelength matches the spacing

(a) Ultraviolet — about 10 to 400 nm→TOO LONG — a hundred to several thousand times the distance between neighbouring atoms; UV and visible light probe electronic transitions, reporting chemistry rather than lattice geometry

(2) Gamma rays→TOO SHORT — the diffracted beams crowd into the undeviated one and the pattern collapses; gamma rays also come from the nucleus and are hard to obtain as a monochromatic, collimated laboratory beam

(c) X-rays — about 0.01 to 10 nm→MATCH — the same order as the 0.1 nm spacing of atomic planes, so the crystal itself acts as a natural three-dimensional diffraction grating

(d) Infrared — 700 nm and upward→TOO LONG — its energies match molecular vibrations, so infrared spectroscopy identifies bonds and functional groups: what a substance is made of, not how its atoms are stacked

Bragg's law — twice the interplanar spacing times the sine of the glancing angle equals a whole number of wavelengths — converts measured diffraction angles straight into lattice spacings. Von Laue demonstrated X-ray diffraction by a crystal in 1912; the Braggs turned it into a method for determining structures, the same method that produced the X-ray photographs of DNA. Being more energetic does not make a probe better; it makes it the wrong length.

Study next

The electromagnetic spectrum arranged by wavelength, with the characteristic use and typical source of each bandBragg's law and the geometry of X-ray diffraction from a crystal latticeCrystal systems, unit cells and lattice parameters in solid-state physics and chemistryX-ray crystallography in biology, including the diffraction photographs behind the structure of DNA and of proteinsElectron and neutron diffraction, and what each reveals that X-ray diffraction cannot

Common traps

Assuming the most energetic radiation must be the best probe, when a wavelength far shorter than the spacing being measured is as useless as one far longer
Confusing spectroscopic techniques, which identify bonds and energy levels, with diffraction techniques, which determine geometrical arrangement
Forgetting the order of magnitude of atomic spacing, which is the single number needed to choose the right band of the spectrum
Associating X-rays only with medical imaging and so overlooking their role as the standard structural probe of the solid state

Questions of this family in MPSC papers give a purpose and ask which radiation serves it, or give a radiation and ask what it is used for, and the answer always depends on matching wavelength to the scale of the phenomenon. X-rays recur in three distinct roles — medical imaging, security screening and crystallography — and it is worth being able to distinguish them. Expect neighbouring items on ultrasound in medicine and industry, on infrared thermal imaging and remote sensing, and on the use of microwaves, since the Commission tests the whole spectrum a band at a time.

Related PYQs

No directly related past PYQ was found.

Practice

practice — not a real PYQ
X-rays rather than visible light are used to determine the arrangement of atoms in a crystal chiefly for which of the following reasons ?
- (a)X-rays carry more energy than visible light
- (b)The wavelength of X-rays is comparable to the spacing between atoms in a crystal
- (c)X-rays are not absorbed by any material
- (d)X-rays travel faster than visible light
Answer(b) The wavelength of X-rays is comparable to the spacing between atoms in a crystal — diffraction resolves a structure only when the wavelength is of the same order as the spacing, and atomic spacings are around a tenth of a nanometre. Greater energy is incidental, X-rays are certainly absorbed by matter, and all electromagnetic radiation travels at the same speed in vacuum.
practice — not a real PYQ
Bragg's law, used in the analysis of crystal structure, relates the wavelength of the radiation to which of the following ?
- (a)The interplanar spacing and the glancing angle of the beam
- (b)The temperature and density of the crystal
- (c)The atomic number and mass number of the atoms
- (d)The refractive index and the critical angle
Answer(a) The interplanar spacing and the glancing angle of the beam — the condition for constructive interference is that twice the spacing between atomic planes multiplied by the sine of the glancing angle equals a whole number of wavelengths, so measuring the angles at which diffracted beams appear yields the spacings directly.