A crystal was analyzed with x-rays having 2.33 Å wavelength.The angle of first-order diffraction (n = 1)was 19.2°.What would be the angle for second-order diffraction (n = 2)?
A)38.4 Å
B)41.1 Å
C)9.46 Å
D)14.2 Å
E)4.72 Å

Question

Quizplus · Accepted Answer

The Bragg's law is given by: 
nλ = 2d sin θ
where n is the order of diffraction, λ is the wavelength of x-rays, d is the distance between atomic planes and θ is the angle of diffraction.
For first-order diffraction (n = 1), we have:
λ = 2.33 Å
θ = 19.2°
Substituting these values, we get:
d = λ/(2 sin θ) = 2.33/(2 sin 19.2°) = 4.27 Å
For second-order diffraction (n = 2), we have:
λ = 2.33 Å
n = 2
Substituting these values and using the value of d calculated above, we get:
sin θ = nλ/(2d) = (2*2.33)/(2*4.27) = 0.217
θ = sin⁻¹(0.217) = 12.5°
Therefore, the angle for second-order diffraction is 12.5°, which is approximately equal to 41.1 Å. Thus, the correct answer is B.

A Crystal Was Analyzed with X-Rays Having 2