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**1. Homework Statement**

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. Homework Equations**

[tex]E_n=\frac{h^2n^2}{8mL^2}[/tex]

**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?

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

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