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 constructive interference occurs when 2dsinθ = nλ, where d is the distance between the planes, θ is the angle of incidence, λ is the wavelength of the X-ray, and n is the order of the diffraction.

For the first order, n = 1, we have:

2dsin20° = 1.4 × 10^-10 m

d = 2.56 × 10^-10 m

For the second order, n = 2, we have:

2dsinθ = 2λ

2dsinθ = 2(1.4 × 10^-10 m)

sinθ = λ/d

sinθ = 2λ/2d

sinθ = λ/(2d/n)

sinθ = λ/(2(2.56 × 10^-10 m)/2)

sinθ = 1.4 × 10^-10 m/(2.56 × 10^-10 m)

θ = 43°

Therefore, the second order line will appear at an angle of 43°. The answer is C.

If an X-Ray Beam of Wavelength 1