# Arithmetic Question Involving Quantum Physics

1. The problem statement, all variables and given/known data

Two adjacent allowed energies of an electron in a one-dimensional box are 2.0 eV and 4.5 eV. What is the length of the box?

2. Relevant equations

$$E_n=\frac{h^2n^2}{8mL^2}$$

3. The attempt at a solution

My question is, since E_n and n^2 are both on separate sides of the equation in the numerator, why can’t I put Delta in front of each of these variables and solve for L?

$$\Delta E_n=\frac{h^2\Delta n^2}{8mL^2}$$ and since the energy levels are adjacent, $$\Delta n^2=1$$

I tried doing this, but it gave me the incorrect answer. I know how I am supposed to do the problem now, I am just wondering why my original technique does not work.

Thanks,
Cooper

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