BITSAT 2024 Shift 1 Paper

The energy of a hydrogen atom is given by the equation:
E=−‌

RH

9

which can also be expressed using the formula for energy levels:
En=−‌

RH

n2

From these equations, we know:
‌n2=9
‌n=3
For 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=9
Thus, the degeneracy of the hydrogen atom with the given energy level is 9 .