The energy levels of a particle in a 1-d box?

Question

The energy levels of a particle in a 1-d box are given by E=n^2h^2/8mL. As the length of the box gets larger:

a) the energy difference between n=1 and n=2 gets larger

b) the energy difference between n=1 and n=2 gets smaller

c) the energy difference between n=1 and n=2 stays constant

d) it will require more energy to excite the particle from n=1 to n=2

Note: more than 1 answer may be right

Answer 1

As L increases, E decreases proportionately.

b, and d.

Edit: I believe option d is poorly stated and should be challenged. If distance is increased, more energy would be require.  

Humans write test questions, and we all make mistakes :-).

Answer 2

There's a mistake in your formula, it should read n^2 h^2 / 8mL^2 - remember that the L is squared.

Anyways, the energy of the level n = 1 is given by

h^2 / (8mL^2)

and that of the level n = 2 is then

4h^2 / (8mL^2)

Therefore, the energy difference is

3h^2 / (8mL^2)

so that as L increases, this difference decreases - i.e, choice b) is correct. Choice d) is equivalent to choice a), so it is not correct.