First slide

Matter waves (DC Broglie waves)

Question

The largest distance between the interatomic planes of a crystal is $10^{- 7}$ cm. The upper limit for the wavelength of X-rays which can be usefully studied with this crystal is

Moderate

A

$1 \overset{o}{A}$
B

$2 \overset{o}{A}$
C

$10 \overset{o}{A}$
D

$20 \overset{o}{A}$

Solution

$\begin{array}{l} Bragg' s law, 2 dsinθ = nλ or λ = \frac{2 dsinθ}{n} \\ For maximum wavelength, n_{\min} = 1, {(sinθ)}_{\max} = 1 \\ ∴ λ_{\max} = 2 d or λ_{\max} = 2 \times 10^{- 7} cm = 20 \overset{o}{A} \end{array}$

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