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## Homework Statement

An electron is confined to a narrow evacuated tube. The tube, which has length of 2m functions as a one dimensional infinite potential well.

A: What is the energy difference between the electrons ground state and the first excitied state.

B: What quantum number n would the energy difference between adjacent energy levels be 1eV - which is measurable, unlike the result of part A.

## Homework Equations

[/B]

[tex]

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

[/tex]

## The Attempt at a Solution

I must not be using the equation correctly, as I am getting values many many orders of magnitudes out. Is m in the equation the mass of the particle? So in this case the mass of the electron?

[tex]

E_1=\frac{\hbar^2 \pi^2 n^2}{2mL^2}= \frac{(1.055 \times 10^{-34})^2 \pi^2 }{2(9.109 \times 10^{-31})2^2} = 1.507 \times 10^{-38} J \\

E_2=\frac{\hbar^2 \pi^2 n^2}{2mL^2}= \frac{(1.055 \times 10^{-34})^2 \pi^2 }{2(9.109 \times 10^{-31})} = 6.03 \times 10^{-38} J \\

\Delta E = E_2 - E_1 = 4.523 \times 10^{-38} J = 2.82 \times 10^{-19} eV

[/tex]

For B: I got a quantum number of around 3.5 billion :D, so I have to be doing something wrong. Also my main question for part B was the bit where it carries on with "- which is measurable, unlike the result of A", I have no idea what they mean by that, so if anyone does I would really appreciate it.

Thanks :)

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