How Do You Calculate Kinetic Energy of Neutrons for Diffraction Analysis?

[louza8]

Homework Statement

Suppose you want to observe neutron diffraction in a crystal with 0.27nm spacing between lattice planes.

Part A asks for the momentum of neutrons with a wavelength equal to the spacing. I used p = h/lambda to get the correct answer 2.5×10−24kgms^-1

Question1:

Find the kinetic energy of neutrons having wavelength equal to this spacing.

Question2:
If these neutrons constituted an ideal gas, what would be the gas temperature?

Homework Equations

Q1. k=0.5mv²
Q2. PV=nRT

The Attempt at a Solution

Q1: I've tried a couple of different methods, don't know if I'm going the right way with this.
k=0.5mv²
0.5(1.67*10^-27)(1.47*10^3)^2 = 1.80*10^-21J

is this correct?
Q2: I have no idea.
Thanks in advance.

 

[ehild]

Q1 is correct.

What is the average kinetic energy of an atom or molecule in an ideal gas?

ehild

 

[louza8]

Ah, cool.

so 0.5mv^2 = (3/2)kT? So just rearrange to get T with k being boltzmann's constant?

Helpful as always ehild. Thanks.

 

[ehild]

I hope it is that easy. Try. ehild

 

[louza8]

correct, thanks