Electron Energy Levels in Nanowire | Approximation & Quantum #s

[Pengwuino]

The question is:

We can approximate an electron moving in a nanowire as a one-dimensional infinite square-well potential. Let the wire be 2 um long. The nanowire is cooled to a temperature of 13K, and we assume the electron’s average kinetic energy is that of a gas molecule at this temperature ( = 3/2 kT). (a) What are the three lowest possible energy levels of the electrons? (b) What is the approximate quantum number of the electrons moving in the wire?

So I have the equation to find the energy in an infinite well…

$$\[ \begin{array}{l} E_n = n^2 \frac{{\pi ^2 (\hbar c)^2 }}{{2mc^2 L^2 }} \\ L = 2*10^3 nm \\ m = 5.11*10^5 eV \\ \hbar c = 197.33eV*nm \\ \end{array} \]$$

Using this, I find n=1 to equal 9.40*10^-8 eV

The book says I am good there.

The problem is when I have to find the second energy level. I figured you use n=2 which means its just 2^2 or 4 times the energy but the book says its just 2 times the energy of the first energy level. What am I not understanding here?

 

[Morlock26]

I'm pretty sure the book made a mistake. For n=2, E2 = 4*E1 = 3.8 X 10^-7. I double checked with cramster, and that's how it was done there also.