# Thread: KE = KbT or 3/2 KbT??

1. Hi all,

Qn: Calculate the De Broglie wavelength of a neutron with a translational kinetic energy = kT at 300K.
k = boltzmann constant = 1.38 x 10^-23 JK-1

Solution:
λ = h / p
= h / (2mE)^1/2 (E: kinetic energy)
= h / (2mkT)^1/2 (substitute E with kT, the translational kinetic energy)

why do we use translational energy = kT here?
I googled, most of the webpage suggest KE = 3/2 kT (or kBT) (kB: boltzmann constant)
I am trying to understand why the question omit 3/2?

To my understanding 3/2 is to account for the 3 axis of direction, am i right? there is x, y, and z direction.
So instead of KE = 1/2 kT, we get 3/2 kT.

Any guidance is appreciated

2. I think the factor of 3/2 represents an average over lots of particles. But there's no reason to expect they will all be the same. Perhaps they said to use kT as it would be the right sort of order of magnitude.

3. i see, thanks Jilan.
I have been learning 3/2kT all my life so i didn't expect them to be different!
But... hey yup there's no reason to expect them all the same... guess you may be right.

Perhaps they just wanted an estimate that give that sort of order of magnitude...

I also wondered if there could be something else taking place that I may not be aware of.
If there are other factors to consider that I missed out...

4. Originally Posted by Feliss
i see, thanks Jilan.
I have been learning 3/2kT all my life so i didn't expect them to be different!
But... hey yup there's no reason to expect them all the same... guess you may be right.

Perhaps they just wanted an estimate that give that sort of order of magnitude...

I also wondered if there could be something else taking place that I may not be aware of.
If there are other factors to consider that I missed out...
One possible answer to your question is that would apply to neutrons in thermal equilibrium. Does your question suggest that the neutrons are in thermal equilibrium, or is it just expressing the kinetic energy of the neutrons in terms of temperature as an exercise?

5. Hi KJW,

Could you explain more about the part on thermal equilibrium?
How would it affect whether the 3/2 term?

Do you mean, that 3/2kT term only applies if the neutron is in thermal equilibirum?
And if not, we can just use an estimate?
Please correct me if i am wrong..

6. What I'm saying is that saying the kinetic energy of the neutrons should be assumes that the neutrons are in thermal equilibrium, where the equipartition principle applies. I'm guessing that the question makes no such assumption and that you are reading too much into the question.

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