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

aaron-physics

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

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)


2. Relevant equations
[itex] \Delta E = E_2-E_1 = \dfrac{n^2h^2\pi^2}{2ml^2} [/itex]

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

3. 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

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

but without knowing [itex] n_1 [/itex] or [itex] n_2 [/itex] I am stuck.

dipole

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