Arithmetic Question Involving Quantum Physics

[Coop]

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?

Homework Equations

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

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

 

[lightgrav]

Delta is shorthand for small change; essentially a derivative.
when you change n^2 to (n+1)^2 , it is not really a small change,
and clearly the change in the second depends on n.
(that is, 1^2 is 1, but 2^2 = 4 ... a difference of 3
5^2 = 25 , but 6^2 = 36 ... a difference of 11 , which is 3½ times as much.