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 ∘ ?

Question

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    ∘   ?

Alden Holder · Accepted Answer

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  λwhere, d= distance between interatomic planesHere   θ is the angle between normal to the plane and incident (and reflected) X - raysTherefore,   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  λGiven:  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   nmAnswer: The required separation between lines is   d  =  0.0576   nm

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

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