1. Meaning of half-filled $f$-orbitals

A half-filled $f$-subshell means: $f^7$ because the $f$-subshell has 7 orbitals and can hold a maximum of 14 electrons.

So we need to identify which given elements have ground-state configuration containing $4f^7$.

2. Write ground-state electronic configurations

For lanthanoids, the relevant part is $4f$, $5d$, and $6s$.

• Pm $(Z=61)$: $[Xe] \, 4f^5 6s^2$

• Sm $(Z=62)$: $[Xe] \, 4f^6 6s^2$

• Eu $(Z=63)$: $[Xe] \, 4f^7 6s^2$ Here, the $f$-subshell is half-filled.

• Gd $(Z=64)$: $[Xe] \, 4f^7 5d^1 6s^2$ Here also, the $4f$-subshell is half-filled.

• Tb $(Z=65)$: $[Xe] \, 4f^9 6s^2$ (more precisely often written as $4f^9 6s^2$, sometimes with $5d^0$) This is not half-filled.

3. Check each element

• A. Sm: $4f^6$ → not half-filled
• B. Eu: $4f^7$ → half-filled
• C. Tb: $4f^9$ → not half-filled
• D. Gd: $4f^7$ → half-filled
• E. Pm: $4f^5$ → not half-filled

So the correct elements are: $\boxed{\text{Eu and Gd}}$

4. Match with given options

Option A: B and D only

This corresponds to Eu and Gd only, which is correct.

5. Comparison with stored correct answer

Stored correct answer = A

Our derived answer = A

So they agree.