Suppose you want to produce a diffraction pattern with X rays whose wavelength is 0.025 nm.

Awainaideannagi 2022-07-20 Answered
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 ?
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Answers (1)

Alden Holder
Answered 2022-07-21 Author has 15 answers
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;
2 d sin ( θ ) = n λ
where, d= distance between interatomic planes
Here θ is the angle between normal to the plane and incident (and reflected) X - rays
Therefore, 2 sin ( θ ) insted of only sin ( θ )
In the given problem, the conditions given are the same as that of x-ray diffraction.
Formula:
2 d sin ( θ ) = n λ
Given:
θ = 14 n = 1 λ = 0.025  nm d = ? d = n λ 2 sin ( θ ) d = 1 × 0.025  nm 2 × sin ( 14 ) d = 0.025 0.434 d = 0.0576  nm
Answer: The required separation between lines is d = 0.0576  nm
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