Question

If an X-ray beam of wavelength 1.4 × 10-10 m makes an angle of 30° with a set of planes in a crystal causing first order constructive interference, what is the plane spacing?

Answer 1

Answer:

Plane spacing, $d=1.4\times 10^{-10}\ m$

Explanation:

It is given that,

Wavelength of x-ray, $\lambda=1.4\times 10^{-10}\ m$

Angle the x-ray made with a set of planes in a crystal causing first order constructive interference is 30 degrees

We need to find the plane spacing. It is based on Bragg's law such that,

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

d is plane spacing

n = 1 here

$d=\dfrac{\lambda}{2\sin\theta}\\\\d=\dfrac{1.4\times 10^{-10}}{2\times \sin (30)}\\\\d=1.4\times 10^{-10}\ m$

So, the plane spacing is $1.4\times 10^{-10}\ m$.