Bragg's Law MCQ - Practice Questions & Answers

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Which of the following relations is correct for first-order Bragg’s diffraction?

$\sin Θ = \frac{2 a}{λ} (h^{2} + k^{2} + l^{2})$

$\sin Θ = \frac{2 a}{λ} {(h^{2} + k^{2} + l^{2})}^{\frac{1}{2}}$

$\sin Θ = \frac{λ}{2 a} {(h^{2} + k^{2} + l^{2})}^{\frac{1}{2}}$

$\sin Θ = \frac{λ}{2 a} {(h^{2} + k^{2} + l^{2})}^{2}$

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Superconductivity and Bragg’s Equation

Superconductivity
Kammerlingh Onnes observed this phenomenon at 4 K in mercury. A substance is said to be superconducting when it offers no resistance to the flow of electricity. There is no substance which is superconducting at room temperature. Superconductors are widely used in electronic power transmission, building super magnets etc. For example, YBa₂Cu₃O₇, Nb₃Ge alloy, (TMTSF)₂PF₆, etc.

Cohesive Energy
It is the energy needed to achieve infinitely separated gaseous ions from one mole of anionic crystal lattice that is negative of the Lattice energy.

$\\\mathrm{MX} \rightarrow \mathrm{M}^{+}+\mathrm{X}\\\mathrm{s}^{\prime} \quad\quad\quad \mathrm{g}^{\prime} \quad\quad \mathrm{g}^{\prime}$

Bragg’s Equation
This equation gives a simple relationship between the wavelength Of X-rays and the distance between the planes in the crystal and the angle Of reflection. This equation can be written as:

$\\\mathrm{n} \lambda=2 \mathrm{d} \sin \theta\\\\ \mathrm{Here} \\\mathrm{n\:=\:Order\:of\:reflection;\:in\:general\:it\:is\:taken\:as\:1.}\\\\\mathrm{\lambda\: =\:Wavelength\:of\:X-rays}\\\\\mathrm{d\: =\:Distance\:between\:two\:layers\:of\:the\:crystals}\\\\\mathrm{\theta\: =\: Angle\:of\:incident\:light}$

As for a given set of lattice planes the value of 'd' is fixed so the possibility of getting maximum reflection depends only on θ. If we increase θ gradually a number of positions will be observed at which there will be maximum reflection.

Bragg’s Application

Bragg's observation has been proved highly beneficial in determining the structures and dimensions of ionic crystalline solids.
It also helped in describing many properties of X-rays also.
It helped in the construction of X-ray spectrometer by which the crystalline structure of crystals can be easily described. For example, face-centred cubic structure of NaCl.