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 for constructive interference is given by:
2d sinθ = nλ
where d is the distance between two adjacent planes in the crystal, θ is the angle of incidence, n is the order of reflection and λ is the wavelength of the x-ray beam.

For first order reflection:
2d sin20° = λ
2d = λ/sin20° = 4.14 × 10^-10 m

For second order reflection:
2d sinθ = 2λ
sinθ = (2λ/2d) = λ/d = 2sin20°
θ = sin^-1(2sin20°) = 43.1°

Therefore, the second order line will appear at an angle of 43.1°. Hence, the correct answer choice is C.

If an X-Ray Beam of Wavelength 1