**Using X-ray Diffraction**

Part A = 0.2130nm

Part B = 69.9°

Part C = No, because the existence of such a maximum produces an unphysical result such as the sine of an angle being greater than one.

**Solution Below:**

The angle of incidence has to be equal to the angle of reflection.

The difference in the beam’s path from a source to an observer for neighboring planes has to be equal to an integer multiple of the wavelength; that is,

2dsin(θ) = mλ (for m = 1, 2, …)

The path difference 2dsin(θ) can be determined from the diagram. The second condition is known as the Bragg condition.

Part A

Express your answer in nanometers to four significant figures.

This is very straightforward. Just use the formula given in the intro:

2dsin(θ) = mλ

2d * sin(28) = 1 * 0.200

d = 0.2130 nm

0.2130 nm

Part B

Express your answer in degrees to three significant figures.

Just use the same formula, only change m to “2″ and use the value of d that you found in Part A:

2d * sin(28) = 1 * 0.200

2 * 0.2130 * sin(θ) = 2 * 0.200

sin(θ) = 0.938967

θ = 69.9°

69.9°

Part C

- Yes, because all crystals have at least three planes.
- Yes, because the diffraction pattern has an infinite number of maxima.
- No, because the angle of a third maximum is greater than 180°.
**No, because the existence of such a maximum produces an unphysical result such as the sine of an angle being greater than one.**

The answer is “No, because the existence of such a maximum produces an unphysical result such as the sine of an angle being greater than one.”

Note that this depends on the inputs for your particular version of the problem. You can use the calculator in Part B to solve for the 3rd maxima, just make “m” equal to 3

No, because the existence of such a maximum produces an unphysical result such as the sine of an angle being greater than one.