Question

You are measuring the lattice constant (the distance between planes of atoms) of a sample crystal using X-ray diffraction. The crystal structure is known to be SC or simple cubic. Your X-ray tube produces X-rays with a wavelength of 0.920 nm. You observe the first diffraction peak at an angle of 20.6°. What is the lattice constant of the crystal?

Answer 1

Lattice constant, d = 1.3 nm

Step-by-step explanation:

It is given that,

Wavelength,
`\lambda=0.92\ nm=0.92* 10^(-9)\ m`

You observe the first diffraction peak at an angle of 20.6°,
`\theta=20.6`

Using Bragg's diffraction law as :

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

Here, n = 1

d = lattice constant

`d=(\lambda)/(2\ sin\theta)`

`d=(0.92* 10^(-9))/(2\ sin(20.6))`

`d=1.30* 10^(-9)\ m`

or

d = 1.3 nm

So, the lattice constant of the crystal is 1.3 nm. Hence, this is the required solution.