JEE Chemistry 2023 Question with Solution

Given: The elements are Sm $(Z = 62)$, Eu $(Z = 63)$, Tb $(Z = 65)$, Gd $(Z = 64)$, and Pm $(Z = 61)$.

Find: Which elements have half-filled $f$-orbitals in the ground state, and hence the correct option.

Half-filled orbitals, such as $4f^7$, are especially stable due to symmetry and exchange energy.

The electron configurations of the elements are as follows:

• $^{62}\text{Sm}: 4f^6 6s^2$
• $^{63}\text{Eu}: 4f^7 5d^1 6s^2$
• $^{65}\text{Tb}: 4f^9 6s^2$
• $^{64}\text{Gd}: 4f^7 5d^1 6s^2$
• $^{61}\text{Pm}: 4f^5 6s^2$

The elements with half-filled $f$-orbitals are therefore Eu and Gd, because both contain $4f^7$.

These correspond to the statement B and D only.

Therefore, the correct option is A.

Given: A half-filled $f$-subshell means exactly $7$ electrons in the $f$-subshell.

Find: Which listed elements have configuration containing $4f^7$.

Check each element:

1. Sm has $4f^6$, so it is not half-filled.
2. Eu has $4f^7$, so it is half-filled.
3. Tb has $4f^9$, so it is not half-filled.
4. Gd has $4f^7$, so it is half-filled.
5. Pm has $4f^5$, so it is not half-filled.

So the correct pair is Eu and Gd.

Among the given options, this is B and D only, hence the correct option is A.