Electron in a box. Finding the length of the box. (infinite well)

[aaron-physics]

Homework Statement

An electron is confined in a one-dimensional box (an infinite well). Two adjacent allowed energies of the electron are 1.068 × 10-18 J and 1.352 × 10-18 J. What is the length of the box? (h = 6.626 × 10-34 J · s, mass of electron = 9.11 × 10-31 kg)

Homework Equations

$\Delta E = E_2-E_1 = \dfrac{n^2h^2\pi^2}{2ml^2}$

n = energy level, h =Planck's constant, m = effective mass, l is the length of the box.

The Attempt at a Solution

I am having a lot of trouble with this problem because they do not give the energy levels the electron moves between. They only say that they are "adjacent".

If they were given I see the length would be

$l = \sqrt{\dfrac{h^2\pi^2}{2m\Delta E} (n^2_2-n^2_1)}$

but without knowing $n_1$ or $n_2$ I am stuck.

 

[dipole]

try writing n2 as n1 + 1 and forming a system of equations