1. Identify the element

   The atomic number is $71$, so the element has $71$ electrons in the neutral state.

2. Write the electronic configuration up to this point

   Using the Aufbau principle, the filling sequence around this region is: $6s \rightarrow 4f \rightarrow 5d$

   Up to atomic number $70$ (ytterbium), the configuration is: $[Xe]4f^{14}6s^2$

3. Add the 71st electron

   The next electron, i.e. the $71^{\text{st}}$ electron, enters the $5d$ orbital.

   So for atomic number $71$ (lutetium), the configuration is: $[Xe]4f^{14}5d^16s^2$

4. Check the options

   • A: $4f$ ❌
   • B: $6s$ ❌
   • C: $6p$ ❌
   • D: $5d$ ✅

Therefore, the $71^{\text{st}}$ electron enters the $5d$ orbital.