Question

The second-order diffraction for a gold crystal is at an angle of 22.20o for X-rays of 154 pm. What is the spacing between the crystal planes?

Answer 1

Answer: The spacing between the crystal planes is $4.07\times 10^{-10}m$

Explanation:

To calculate the spacing between the crystal planes, we use the equation given by Bragg, which is:

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

where,

n = order of diffraction = 2

$\lambda$ = wavelength of the light = $154pm=1.54\times 10^{-10}m$     (Conversion factor:  $1m=10^{12}pm$ )

d = spacing between the crystal planes = ?

$\theta$ = angle of diffraction = 22.20°

Putting values in above equation, we get:

$2\times 1.54\times 10^{-10}=2d\sin (22.20)\\\\d=\frac{2\times 1.54\times 10^{-10}}{2\times \sin (22.20)}\\\\d=4.07\times 10^{-10}m$

Hence, the spacing between the crystal planes is $4.07\times 10^{-10}m$