Single Choice

For Bragg's diffraction by a crystal to occur, then which of the following is correct for the X-ray of wavelength $$\lambda$$ and interatomic distance d :

A$$\lambda$$ is greater than $$2d$$
B$$\lambda$$ equals $$2d$$
C$$\lambda$$ is smaller than or equal to $$2d$$
Correct Answer
D$$\lambda$$ is smaller than $$2d$$

Solution

The condition for Bragg's diffraction is
$$2dsin\theta=n\lambda$$
$$\implies sin\theta=\dfrac{n\lambda}{2d}\leq 1$$
$$\implies \lambda\leq \dfrac{2d}{n}$$
where $$n$$ is a positive integer
Hence the maximum value of $$\lambda$$ occurs for $$n=1$$.
Hence $$\lambda\leq 2d$$

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