Energy requirements between orbitals

[ChiliPanda]

Homework Statement

I've already done all of the work, the answer I received just seemed odd, so a friend recommended I ask you guys to check over it. The problem was to determine the atomic spectrum of hydrogen and determine the energy (in EV) required to move between orbitals.
I got the following answers - 2>1 (ultraviolet) 10.2 EV, 3>2 (red) 1.9 EV, 4>2 (blue-green) 2.5 EV, 5>2 (violet) 2.9EV, and 6>2 (deep violet) 3 EV.

The thing that seemed "odd" to me is that it takes the most energy to move an electron from the ground state to orbital 2. I know that it takes energy to move electrons away from the nucleus because of the attraction force, but I always figured it would take more energy the further it was pulled away, such as when stretching out a rubber band, until the electron had so much energy that it could break off. Thus, I think somehow I messed up somewhere along the way.

Homework Equations

I got the EV calculations from the formula E=12400/λ, where λ is wavelength in angstroms which I got from a spectrometer.

 

[Ygggdrasil]

I don't know if the numbers are correct, but the pattern is. The spacings between energy levels do decrease as one gets farther from the nucleus (i.e. n increases). The way to think of it is that electrons are bound in an atom by the electric attraction to the positively charged nucleus. The strength of electrostatic attraction decreases with distance (remember Coulomb's law), so as the electron goes farther away from the nucleus, the easier it is to move it away.

 

[ChiliPanda]

thanks much for the confirmation!