Single electrons travelling at 550 ms^-1 are passed through a diffraction grating with a spacing between the slits of 2.5 micrometers. What would the angle between the zeroth and first maximum of the resulting interference pattern be?

This is a question based loosely around the specification of the OCR A-Level Physics B course, requiring the student to recall two important quantum mechanical relations, first with one from the A2 part of the course and then with one from the AS part of the course. The first step towards tackling the question requires the student to calculate the de Broglie wavelength of the electron, using the relation lambdadB = h/mev (the mass of the electron and Planck's constant would need to be looked up, or given in an exam). By plugging in v = 550 ms^-1 and the values of the two constants into this equation a de Broglie wavelength of 1.3 micrometers (2 s.f.) should be obtained. The student would then need to recognise that this wavelength can be used with the relation n * lambda = sin(theta) * d to calculate the required angle. Plugging in n = 1 (for we are only considering the zeroth to the first maximum, i.e. a path difference of 1 wavelength), d = 2.5 micrometers, and lamdba = 1.3 micrometers into this equation a value for theta of 32 degrees (2 s.f.) should be obtained, which is the answer to the question.