Question

An x-ray beam with wavelength 0.240 nm is directed at a crystal. As the angle of incidence increases, you observe the first strong interference maximum at an angle 21.0 ��. What is the spacing d between the planes of the crystal? Find the angle ��2 at which you will find a second maximum.

Answer 1

To find the spacing between the planes of the crystal, Bragg's Law is used with the given X-ray wavelength and the observed angle of the first interference maximum. The same law then allows us to find the angle at which the second maximum will be observed.

Step-by-step explanation:

The question involves using Bragg's Law, which relates the angle of incident X-rays to the spacing between crystal planes. The first strong interference maximum, or first-order diffraction, occurs when the path difference is equal to the wavelength (nλ = 2d sin θ), where n=1. Given the X-ray wavelength is 0.240 nm, and the first maximum is observed at an angle of 21.0°, we can find the spacing, d, using the Bragg equation:

1×0.240 nm = 2d sin(21.0°)

We can rearrange this to solve for d:

d = (1×0.240 nm) / (2 sin(21.0°))

Once we have the value of d, the second-order maximum will be for n=2. We can then solve for the second angle, θ2, using the same Bragg equation:

2×0.240 nm = 2d sin(θ2)

Rearranging for θ2:

sin(θ2) = (2×0.240 nm) / (2d)

And then calculating the inverse sine to find the angle.