Question

The spacing between the principal planes of a crystal is $4\,\mathring{A}$. It is found that first order brag reflection of a beam of monochromatic $X$-rays occurs at an angle of $30^{\circ}$. The wavelength of $X$-rays is

• A. $4\,\mathring{A}$
• B. $2\,\mathring{A}$
• C. $1\,\mathring{A}$
• D. $1.5\,\mathring{A}$

Answer 1

Answer: (A)

Using the Braggs formula $2 d \sin \theta=n \lambda$
where $d =$ distance between diffracting planes.
We can determine the wavelength of these waves,
$2 \times 4 \times 10^{-10} \sin 30^{\circ}$
$=\lambda 8 \times 10^{-10} \times \frac{1}{2}$
$=\lambda 4 \times 10^{-10}=\lambda \lambda$
$= 4\,\mathring{A}$