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Angle at which second-order diffraction will occur in an X-ray spectrometer when X-rays of 200 pm are diffracted by the atoms of a crystal having distance between the two planes as 400 pm is

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30°

60°

45°

90°

answer is A.

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Detailed Solution

For nth order diffraction, $n λ = 2 asin θ$

$∴ \sin θ = \frac{n λ}{2 a}$

n = 2

$∴ \sin θ = \frac{λ}{a} = \frac{200 pm}{400 pm} = \frac{1}{2}$

$∴ θ = \sin^{- 1} (\frac{1}{2}) = 30^{\circ}$

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