Counting States / Uncertainty principle

[positron]

I have a question about an example in my physics notes. It considers Nitrogen at room temperature and calculates p*r and finds this to be greater than h-bar and so it is consistent with the uncertainty principle:
p*r = 2.4*10^-26 > hbar = 1*10^-27

It says at room temperature the momentum can be specified to a reasonable fraction of the typical momentum and the position to about a molecular size and still be consistent with qm and the uncertainty principle. what does this mean?

The mass they used was 28*mass of a proton, but what about the neutrons (or is it okay just for an estimation to use only the neutrons?) I thought that it was deltap and deltar in the uncertainty principle equation, not p or r.

 

[DrClaude]

Using $p$ as the value of $\Delta p$ allows to consider a worse case scenario, since it would mean that you can't even differentiate between a stationary molecule and one that is moving with thermal energy. Multiplying that by the size of the molecule and still respecting the uncertainty principle means that the molecule can be treated classically.

It says at room temperature the momentum can be specified to a reasonable fraction of the typical momentum and the position to about a molecular size and still be consistent with qm and the uncertainty principle. what does this mean?

I realize now I basically just repeated this, but hopefully putting it in other words will help.

The mass they used was 28*mass of a proton, but what about the neutrons (or is it okay just for an estimation to use only the neutrons?)

It is an estimate. It also doesn't take into account the binding energy of the nucleus, but this is more than good enough for most calculations.