Certain planes of a crystal of halite have a spacing of 0.399 nm.The crystal is irradiated by a beam of x-rays.First order constructive interference occurs when the beam makes an angle of 20° with the planes of the crystal surface.What angle does the beam make with the crystal planes for second order constructive?
A)37°
B)40°
C)43°
D)46°
E)49°

Question

Quizplus · Accepted Answer

For first order constructive interference, we have:

dsinθ = λ

where d = 0.399 nm is the spacing between the planes, θ = 20° is the angle between the plane and the incident beam, and λ is the wavelength of the x-rays.

Solving for λ, we get:

λ = d/sinθ = 0.399 nm/sin(20°) = 1.158 nm

For second order constructive interference, we have:

2dsinθ = mλ

where m = 2 is the order of the interference.

Solving for θ, we get:

sinθ = mλ/2d = (2)(1.158 nm)/(2)(0.399 nm) = 5.79

This is the sine of the angle, so we need to take the inverse sine to get the angle itself:

θ = sin⁻¹(5.79) = 43.1°

Therefore, the beam makes an angle of 43.1° with the crystal planes for second order constructive interference, and the best choice is (C).

Certain Planes of a Crystal of Halite Have a Spacing