To solve the problem, we need to understand the penetration power of orbitals towards the nucleus.
1. Penetration Power of Orbitals:
The penetration power of orbitals refers to their ability to get closer to the nucleus. Orbitals with lower angular momentum (like $s$ orbitals) have higher penetration power because they are spherically symmetric and can approach the nucleus more easily. On the other hand, orbitals with higher angular momentum (like $d$ or $f$ orbitals) have lower penetration power, as they are more spread out and less likely to penetrate close to the nucleus.
2. Comparing the Orbitals:
- The $4s$ orbital has the highest penetration power towards the nucleus because it is spherical and has the least angular momentum.
- The $4p$ orbital has a lower penetration power compared to $4s$.
- The $4d$ and $4f$ orbitals have the least penetration power as they have higher angular momentum and are more diffuse.
Final Answer:
The orbital with more penetration power towards the nucleus is $ {4s} $.