A beam of X-rays of different frequencies is reflected at 10 degrees off a crystal of interatomic spacing 0.2 nm. Which X-ray wavelength is preferentially reflected?
A)0.0943 nm
B)0.139 nm
C)0.0695 nm
D)1.02 × 10−10 m
E)3.47 × 10−11 m

Question

Quizplus · Accepted Answer

The Bragg's Law equation is given by:
nλ = 2d sin(θ)
where,
n = order of reflection
λ = wavelength of X-ray
d = interatomic spacing
θ = angle of incidence

We want to find the wavelength that is preferentially reflected, which means the wavelength that satisfies the Bragg's Law equation for the first order of reflection (n=1) and at the given angle of incidence (θ=10 degrees).

Substituting the given values, we get:
1λ = 2(0.2 × 10^-9 m)sin(10 degrees)

Solving for λ, we get:
λ = 0.0695 nm

Therefore, the wavelength preferentially reflected is 0.0695 nm, which corresponds to choice C.

A Beam of X-Rays of Different Frequencies Is Reflected at 10