A certain Crystal has a set of planes spaced 0.30 nm apart. A beam of neutrons s

Question

A certain Crystal has a set of planes spaced 0.30 nm apart. A beam of neutrons strikes the crystal at normal incidence and the first maximum of the diffraction occurs at ?=42 degree. (a) What is de-Broglie wavelength of neutron beam? (b) What should be moment and kinetic energy of the neutron beam?

Explanation / Answer

d = 0.30 nm f = 42? Now, my text has the following relation: n? = D sinf and then this one: d = D sina where 2a = f ==> a = f/2 So I wanted D, and I did this: D = d/sin(f/2) ' which gave me an answer of: 0.837 nm for D. I then plugged this in to n? = D sinf (with n = 1) and got: 0.560 nm. My concern is that the text got an answer of 0.523 nm, and they used a slightly different method. However, I see no reason why my method shouldn't work. Hopefully, someone can explain where my reasoning was flawed. Anyway, for the second part, I did this: ? = h/v(2mE) * h is Planck's constant * mass of neutron is 1.67 x 10^-27 kg

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