00:01
In this exercise, we have the lyman series, which happens when an electron jumps from the end energy level in the hydrogen atom to the first one, and in the process it emits a photon.
00:13
And our job here is to find what are the three longest wavelengths emitted in the lyman series.
00:20
So we have the first energy level, the ground state, has an energy of minus 13 .6 electron volts for the hydrogen.
00:30
An atom.
00:32
And for the nth state, we have that the energy is going to be minus 13 .6, the energy of the ground state divided by n squared.
00:43
So that the energy of the released photon by conservation of energy is going to be the energy of the nth level, the initial energy, minus the final energy, which is the energy of the first level.
00:59
So this is going to be 13 .6.
01:03
1 minus 1 over n squared.
01:10
And since the energy of the photon can be written by hc over lambda, i'm just going to make these two quantities equal.
01:17
So this means that i can isolate lambda in this formula to get lambda equals hc over 13 .6 1 minus 1 over n squared.
01:37
And since hc is 1 ,140 electrons volts nanometers, we're going to make this division here, 1 minus 1 over n squared, which means that lambda equals 91 .18 nanometers over 1 minus 1 over n squared...