Question

The p12 of hw4 asks whether energy level of -1.342*10^-12 J is an allowed electron energy state for atomic hydrogen. From that we get n=4 and the answer is yes. How do we know n=4 is allowed?

Answer 1

Energy levels are quantized. Only (positive?) whole number values of n and Z are allowed.

Answer 2

Can it go indefinitely though? Any positive whole number will be ok then?

Answer 3

Yes, the quantum numbers can go to infinity, but for most (all?) quantum mechanical models, the spacing of the energies get closer together as the quantum number increases, so the energy asymptotically approaches some given energy. The allowed values for quantum numbers depends on the specific quantum mechanical model. For atoms, there are 4 quantum numbers, n, l, ml, ms. N can be any number 1 or greater, l can range from 0 to n-1, and ml can range from -l to l (so it can be both positive and negative). ms is the spin quantum number and has allowed values of plus or minus 1/2.

Answer 4

I suppose what I find confusing, is that hydrogen belongs to n=1 shell on the periodic table, which is why I thought that anything bigger than 1 indicates free electron (for hydrogen obviously). What am I getting wrong?

Answer 5

ofcourse, n=4 is allowed but it 'll be 3rd excited state for H atom while n=1 is the ground state for the same..