X-ray diffraction: 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

The Bragg's law states that nλ = 2d sinθ, where n is the order of diffraction, λ is the wavelength of the X-ray beam, d is the distance between the planes, and θ is the angle of incidence.

For the first order diffraction, n = 1 and θ = 20°. Therefore,

1.4 × 10^-10 m = 2d sin20°

Solving for d gives d ≈ 2.55 × 10^-10 m.

For the second order diffraction, n = 2 and we need to find θ. Using the same equation, we have

2 × 1.4 × 10^-10 m = 2(2.55 × 10^-10 m) sinθ

Solving for sinθ gives sinθ ≈ 0.866, which corresponds to an angle of θ ≈ 43°. Therefore, the second order line will appear at an angle of 43°.

The correct answer choice is C.

X-Ray Diffraction: If an X-Ray Beam of Wavelength 1