# Finding quantum number n of molecule

## Homework Statement

A nitrogen molecule (N2) has a mass of 4.68 x 10-26 kg. It is confined to a onedimensional
box of length L = 100 nm. What is the approximate quantum number n of
the molecule if it has a kinetic energy equal to the thermal energy kBT at room
temperature? What is n if it has a thermal energy corresponding to T = 1 K?

## Homework Equations

$$E_n=n^2\frac{\pi^2\hbar^2}{2mL^2}$$

## The Attempt at a Solution

Well it seemed like it was just plug and chug, but I'm getting an answer that I don't like. I'm getting an answer for n = 1x1014. That seems way too big.

The units also don't make sense.
According to the formula we have...
$$j=\frac{j^2s^2}{kg(nm)^2}$$

But after just seeing an example, I see that that same formula can have c2 in both the numerator and denominator to make the units work out. But I still have the problem of having a huge quantum number. Is that number supposed to be that big?

Thanks

edit: oh and also in that example, it seems as though they converted the mass into electron volts using e=mc2, so I did the same thing and found the quantum number to be even higher. Now I'm getting 1.58x1015. Is that a legitimate quantum number? I was thinking I would get small integers, like 1,2,3,4,etc.

Thanks.

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