The energy of a hydrogen atom is given by the equation:
E=−‌which can also be expressed using the formula for energy levels:
En=−‌From these equations, we know:
‌n2=9‌n=3For
n=3, the possible values of the azimuthal quantum number
l are 0,1 , and 2 , which correspond to the
3 s,3p, and 3d sub-shells, respectively.
The number of orbitals (which indicates the degeneracy) in each sub-shell is:
3s: 1 orbital
3p:3 orbitals
3d: 5 orbitals
Adding these gives the total degeneracy:
1+3+5=9Thus, the degeneracy of the hydrogen atom with the given energy level is 9 .