00:01
In this exercise, we have to compare the radii of a helium atom and a hydrogen atom, such that each one is in an energy level, such that the energy of the level of the helium, which i'm going to call m, is equal to the energy of the level of the hydrogen, which i'm going to call n.
00:27
So the first thing we're going to have to remember is that the energy, of the nth level of a hydrogen like atom is given by minus z squared, z is the atomic number divided by n squared, times the ground state energy of the hydrogen atom.
00:47
So for the helium, we're going to have em equals minus two squared, minus four, eh1 divided by m squared, while for the hydrogen, we're going to have en equals minus e1hn squared.
01:10
And we want to find m as a function of n such that the two energies are the same.
01:18
So we're going to simply make the two energies be the same by requiring that for eh1 divided by m squared.
01:29
Equals e1, eh1 divided by n squared.
01:34
The energy is, the ground state energies cancel out.
01:38
And we get that m equals 2n.
01:45
So if a hydrogen atom is in the nth level and it has a certain energy, then a helium atom in the level 2n will have the same energy.
01:59
That's the conclusion we can draw from here.
02:01
So now let's compare the radii of the helium atom at the 2n level and the hydrogen atom at the end level...