If an x-ray beam of wavelength 1.4 × 10^-10 m makes an angle of 20° with a set of planes in a crystal causing first order constructive interference, at what angle will the second order line appear? A) 40° B) 20° C) 43° D) 4.0° E) 11°

Question

Quizplus · Accepted Answer

We can use Bragg's law to solve this problem:
nλ = 2d sinθ
Where n is the order of diffraction, λ is the wavelength of the radiation, d is the distance between the planes in the crystal, and θ is the angle of incidence.
For the first order diffraction:
1.4 × 10^-10 m = 2d sin20°
Solving for d, we get:
d = 2.28 × 10^-10 m
For the second order diffraction, n = 2:
1.4 × 10^-10 m = 2(2.28 × 10^-10 m) sinθ
Solving for θ, we get:
θ = 43°
Therefore, the second order line will appear at an angle of 43°. The correct answer is (C).

If an X-Ray Beam of Wavelength 1