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

Answer:

Lattice constant, d = 1.3 nm

Explanation:

It is given that,

Wavelength, $\lambda=0.92\ nm=0.92\times 10^{-9}\ m$

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

$d=\dfrac{\lambda}{2\ sin\theta}$

$d=\dfrac{0.92\times 10^{-9}}{2\ sin(20.6)}$

$d=1.30\times 10^{-9}\ m$

or

d = 1.3 nm

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