Question

Certain planes of a crystal of halite have a spacing of 0.399 nm. The crystal is irradiated by a beam of x-rays. First order constructive interference occurs when the beam makes an angle of 20° with the planes. What is the wavelength of the x-rays?

Answer 1

The wavelength of x-ray is 0.272 nm.

Step-by-step explanation:

Inter planer spacing, d = 0.399 nm = 3.99 × 10⁻¹⁰ m

First order constructive interference occurs when the beam makes an angle of 20° with the planes. We need to find the wavelength of the x-rays. The condition for constructive interference is given by :

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

Here, n = 1

`\lambda=2* 3.99* 10^(-10) m\ sin(20)`

`\lambda=2.72* 10^(-10)\ m`

`\lambda=0.272\ nm`

So, the wavelength of the x-rays is 0.272 nm. Hence, this is the required solution.