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

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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 other options are wrong — (a) 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.  (b) 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.  (d) 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.

State PCS 2024 Q56 — Science & Technology PYQ with Answer

State PCS 2024 Q56 — Science & Technology PYQ with Answer