KE = KbT or 3/2 KbT??

[Feliss]

Hi all,

This is my first time here, please help me along

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, x, y, and z direction.
So instead of KE = 1/2 kT, we get 3/2 kT.

Any guidance is appreciated!

[decraig]

Hi all,

 

This is my first time here, please help me along

 

Any guidance is appreciated!

 

Ok. I'm not very good at thermo, at all, but this has to do with the partitioning of energy. Different gasses have different degrees of energy 'freedom'. By freedom, the thermo guys mean the count of the different states of motion and internal motion of molecules in a gas. Oxygen, which is the predominate gas in the atmosphere in this geological age, can do a few things. The two atoms comprising oxygen can oscillate away and then to each other, and they can also spin about their center-of-mass. The equation would be different with an atmosphere of, say, C02 that does not have the axial symmetry of oxygen.

Edited November 23, 2013 by decraig

[swansont]

It could simply be a typo, because you are correct. You should get 1/2 kT for each degree of freedom. It's also possible it was an estimate where a factor of 2 is not deemed to be of much consequence.

 

 

 

Ok. I'm not very good at thermo, at all, but this has to do with the partitioning of energy. Different gasses have different degrees of energy 'freedom'. By freedom, the thermo guys mean the count of the different states of motion and internal motion of molecules in a gas. Oxygen, which is the predominate gas in the atmosphere in this geological age, can do a few things. The two atoms comprising oxygen can oscillate away and then to each other, and they can also spin about their center-of-mass. The equation would be different with an atmosphere of, say, C02 that does not have the axial symmetry of oxygen.

 

Feliss already indicated that s/he understood degrees of freedom.

[decraig]

deleted

Edited November 23, 2013 by decraig

[Feliss]

Thanks swansont,

I thought something else could be happening that I may not be aware of.

But alrighty yup it could just possibly be an estimate...

 

And thanks Decraig too You got me thinking some stuff about partitioning of energy...