Mastering Physics Solutions: Exercise 24.37

Exercise 24.37

Part A = 2.1 * 10^-9 m Click to use the calculator/solver for this part of the problem

Solution Below:

A certain crystal gives a deflection angle of 22° for the first-order maximum of monochromatic X-rays with a frequency of 1.9*10^17 Hz.

Part A

What is the lattice spacing of the crystal?
Express your answer using two significant figures.

Use Bragg’s law for this problem:

n * λ = 2 * d * sin(θ)

Note that n = 1 (since this is a first order wavelength)

Start by figuring out the wavelength (λ):

c = λf
2.998 * 10^8 m/s = λ * 1.9 * 10^17 Hz
λ = 1.578 * 10^-9 m

So:

n * λ = 2 * d * sin(θ)
1 * 1.578 * 10^-9 = 2 * d * sin(22)
1.578 * 10^-9 = 2 * 0.37461 * d
1.578 * 10^-9 = 0.7492 * d
d = 2.106 * 10^-9 m

2.1 * 10^-9 m

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