Question

Number of degenerate orbitals present in the first excited state of he+ ion is

Answer 1

Answer: -

Four fold degenerate

Explanation: -

He⁺ is a hydrogen like species.

For them all orbitals belonging to the same shell having the same principal quantum number are having same energy as per Bohr energy expression

E = - $\frac{Z2me4}{8n2h2ε2}$

Thus energy of 2s orbital is same as of 2p.

The ground state electronic configuration of He⁺ = (1 s 1)

The first excited state of He⁺ is (1 s 0 2 s 1) or (1 s 0 2 p x 1) or (1 s 0 2 p y 1) or (1 s 0 2 p z 1).

Since all of them have the same energy, we can see it is 4 fold degeneracy.

Answer 2

Answer:

Total no of degenerate orbitals present in first excited state ie: 2nd  shell are 4 orbitals.

Explanation:

This is because in case of hydrogen atom and hydrogen like species energy of electron is directly proportional to (n) and as result 2s, 2p orbitals  would be having the same energy inspite of their different shapes of atomic orbitals.

no of orbitals is 2s subshell - 1 orbital

2p- 3 orbitals.

Therefore 4 fold degeneracy!