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Chapter 32: Problem 47

X-ray diffraction in potassium chloride (KCl) results in a first order maximum when 97 -pm-wavelength \(\mathrm{X}\) rays graze the crystal plane at \(8.5^{\circ} .\) Find the spacing between crystal planes.

Short Answer

Expert verified
The spacing between the crystal planes is approximately \(2.78 \times 10^{-10}\) m (or 278 pm).

Step by step solution

01

Identify the knowns

From the problem, we know that the wavelength (\(\lambda\)) of the X-rays is 97 pm, which is \(97 \times 10^{-12}\) m. The order of diffraction (n) is 1, and the angle of incidence (\(\theta\)) is \(8.5^{\circ}\). We are asked to find the distance between the crystal planes (d).
02

Apply Bragg's Law

Bragg's law states \(n\lambda=2d\sin\theta\). Substituting the provided values, we get \(1 \times (97 \times 10^{-12}\) m\) = \(2d\sin(8.5^{\circ})\).
03

Solve for d

To find the spacing between the crystal planes (d), we rearrange the formula to get \(d = \frac{n\lambda}{2\sin\theta}\). Substituting the given values into the formula gives us \(d \approx \frac{1 \times 97 \times 10^{-12}\) m}{2\sin(8.5^{\circ})\). Calculating this provides us with the spacing between the crystal planes.

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Most popular questions from this chapter

Light with wavelength \(633 \mathrm{nm}\) is incident on a \(2.5-\mu \mathrm{m}\) -wide slit. Find the angular width of the central peak in the diffraction pattern, taken as the angular separation between the first minima.

You can hear around corners, but you can't see around corners. Why?

A double-slit experiment has slit spacing \(0.12 \mathrm{mm}\). (a) What should be the slit-to-screen distance \(L\) if the bright fringes are to be \(5.0 \mathrm{mm}\) apart when the slits are illuminated with 633 -nm laser light? (b) What will be the fringe spacing with 480 -nm light?

A five-slit system with \(7.5-\mu \mathrm{m}\) slit spacing is illuminated with 633 -nm light. Find the angular positions of (a) the first two maxima and (b) the third and sixth minima.

Find the minimum angular separation resolvable with \(633-\mathrm{nm}\) laser light passing through a circular aperture of diameter \(2.1 \mathrm{cm} .\)
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