Question

The structure of the NaCl crystal forms reflecting planes 0.541 nm apart. What is the smallest angle, measured from these planes, at which constructive interference of an X-ray beam reflecting off the two planes is observed?

Answer 1

Answer:

$\theta=4.5^{\circ}$

Explanation:

Given that,

The distance between reflecting planes is 0.541 nm, d = 0.541 nm

Let the wavelength is 0.085 nm

We need to find the smallest angle, measured from these planes, at which constructive interference. Using Bragg's equation to find it as follows :

$m\lambda=2d\sin\theta$

For smallest angle, m = 1

$\theta=\sin^{-1}(\dfrac{m\lambda}{2d})\\\\\theta=\sin^{-1}(\dfrac{1\times 0.085\ nm }{2\times 0.541\ nm })\\\\\theta=4.5^{\circ}$

So, the smallest angle is 4.5 degrees.