Question

For a hydrogen atom or one-electron ion, how many atomic orbitals share the same principle quantum number n?

a) n - 1

b) n + 1

c) 2n

d) n^2

Answer 1

when

n = 1 the number of atomic orbitals = 1 = 1^2

and

when n = 2

then number of atomic orbitals = 2 for 2s orbital + 3 for 3p orbital = 4 = 2^2

and

when n = 3 then number of atomic orbitals = 1 for 3s + 3 for 3p orbital + 5 for 3d orbital = 9 = 3^2

thus

general formula is n^2 where n = principal quantum number.

option d) n^2 is the answer.