Question

In a multi-electron atom, which of the following orbitals, described by the three quantum numbers, will have the same energy in the absence of magnetic field and electric field?
(i) $n=1,l=0,m=0$
(ii) $n=2,l=0,m=0$
(iii) $n=3,l=1,m=1$
(iv) $n=3,l=2,m=1$
(v) $n=3,l=2,m=0$.

• A. (i) and (ii)
• B. (ii) and (iii)
• C. (iv) and (v)
• D. (iii) and (iv)

Answer 1

The correct option is C (iv) and (v)

In a multi-electron atom, orbitals (IV) n $=$ 3, l $=$ 2, m $=$ 1 and (V) n $=$ 3, l $=$ 2,m $=$ 0 will have the same energy as energy corresponds to $(n+l)$ value.

These sets of quantum numbers refer to 3d orbitals.

They have different m values but the sum $(n+l)$ is same ( equal to $3+2=5)$. Hence, they have the same energy.

Hence, the correct option is $C$