X-rays of fixed wavelength yield a first-order maximum at a grazing angle of 12$^{\circ}$.At what angle would one expect to find the corresponding 3^rd order maximum? A) 4.0$^{\circ}$ B) 12$^{\circ}$ C) 36$^{\circ}$ D) 39$^{\circ}$ E) more information is needed

Question

Quizplus · Accepted Answer

The angle for the nth order maximum is given by the equation nλ = 2d sin(θ). For the 3rd order maximum, the angle is 3 times the angle for the 1st order maximum, so 3 * 12° = 36°. However, due to the periodic nature of the sine function, the angle is slightly larger, making it 39°.

X-Rays of Fixed Wavelength Yield a First-Order Maximum at a Grazing