De Broglie wavelength from scattering of neutrons on crystal

[kachilous]

Homework Statement

A certain crystal has a set of planes 0.33 nm apart. A beam of neutrons strikes the crystal at normal incidence and the first maximum of the diffraction pattern occurs at ∅= 38°. What is the de Broglie wavelength of the neutrons?

Homework Equations

nλ = Dsin∅ where D = d / sinα and α = ∅/2

The Attempt at a Solution

First, I found D: D = .33nm / (sin(38/2)) = 1.014
This D corresponds to the spacing of the atoms and the d given in the problem statement
corresponds to the spacing of the planes in the crystal.

I assume n = 1. Then λ = 1.014 nm * sin(38) = .624
The answer .59. What am I doing wrong?

The only thing that I can think of that I might be doing wrong is my n is incorrect.

 

[haruspex]

nλ = Dsin∅ where D = d / sinα and α = ∅/2

First, I found D: D = .33nm / (sin(38/2)) = 1.014
This D corresponds to the spacing of the atoms and the d given in the problem statement
corresponds to the spacing of the planes in the crystal.

There's some confusion here between d and D. Make sure you have clear in your head what each of these is.
Looks to me like you only need your first equation.
Btw, n=1 is not an assumption - it is implied by first maximum.