Awainaideannagi

2022-07-20

Suppose you want to produce a diffraction pattern with X rays whose wavelength is 0.025 nm. If you use a diffraction grating, what separution between lines is needed to genorate a pattern with tne first maximum at an angle of ${14}^{\circ }$ ?

### Answer & Explanation

Alden Holder

X-ray diffraction :
In the case of X-ray diffraction crystal is used instead of the diffraction grating. The crystal consists of an array of equally spaced atoms that act as a grating. The incident light is used in such a way that its wavelength is comparable with an interatomic plane of the crystal.
When such a x-ray incident on the crystal at a particular angle then it reflects at different planes of the atom. The reflected rays for a particular set of planes interfere with each other. If these reflected rays interfere constructively it gives x-ray signal i.e. sharp peak.
The condition to get this pattern/peak is;
$2d\mathrm{sin}\left(\theta \right)=n\lambda$
where, d= distance between interatomic planes
Here $\theta$ is the angle between normal to the plane and incident (and reflected) X - rays
Therefore, $2\mathrm{sin}\left(\theta \right)$ insted of only $\mathrm{sin}\left(\theta \right)$
In the given problem, the conditions given are the same as that of x-ray diffraction.
Formula:
$2d\mathrm{sin}\left(\theta \right)=n\lambda$
Given:

Answer: The required separation between lines is

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