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Chapter 9: Problem 50

X rays of wavelength 2.63 Å were used to analyze a crystal. The angle of first-order diffraction \((n=1\) in the Bragg equation) was 15.55 degrees. What is the spacing between crystal planes, and what would be the angle for second- order diffraction \((n=2) ?\)

Short Answer

Expert verified
The spacing between crystal planes is approximately \(6.11 Å\), and the angle for second-order diffraction is approximately \(25.81°\).

Step by step solution

01

Compute the value of d

From the equation above, we use a calculator to compute the value of d: \(d ≈ 6.11 Å\) So, the spacing between crystal planes is approximately 6.11 Å. #Step 2: Find the angle for second-order diffraction (n=2)# In this step, we will use the Bragg's law equation and the spacing value obtained in the previous step to find the angle for the second-order diffraction, where \(n = 2\). The new equation becomes: \(2\cdot 2.63 Å = 2(6.11 Å)\sin{\theta_2}\) Now we will solve for \(\theta_2\): \(\sin{\theta_2} = \frac{2\cdot 2.63 Å}{2(6.11 Å)}\)
02

Compute the value of \(\theta_2\)

From the equation above, we use a calculator to compute the value of sin(\(\theta_2\)): \(\sin{\theta_2} ≈ 0.4314\) Now, use sin.backwardfunction (inverse sin, arcsin) to find the value of \(\theta_2\): \(\theta_2 ≈ \arcsin(0.4314)\) \(\theta_2 ≈ 25.81°\) So, the angle for second-order diffraction is approximately 25.81 degrees.

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