An x-ray beam of a certain wavelength is incident on a crystal, at 30.7° to a certain family of reflecting planes of spacing 33.4 pm. If the reflection from those planes is of the first order, what is the wavelength of the x rays?
An x-ray beam of a certain wavelength is incident on a crystal, at 30.7° to a certain family of reflecting planes of spacing 33.4 pm. If the reflection from those planes is of the first order, what is the wavelength of the x rays?
Answer:
The wavelength of the x rays is 34.104 pm
Explanation:
Given data:
θ = incidence angle = 30.7°
d = space between planes = 33.4 pm = 33.4 x10⁻¹²m
According Bragg’s expression:
[tex]n\lambda =2dsin\theta \\n=1,first-order\\\lambda = 2dsin\theta\\\lambda =2*33.4*sin30.7=34.104pm[/tex]
Answer:
λ=34.068pm
Explanation:
Wavelength λ=2dsinθ
λ=2(33.4pm)sin30.7
λ=2(33.4pm) * 0.510
λ=66.8* sin30.7
λ=66.8*0.510
λ=34.068pm
X-rays are usually produced by charged particles that are accelerating or decelerating such as a beam of electrons striking a metal plate in an X-ray tube.