The s orbitals (1st, 4th, and 2nd orbitals) are lowest in energy when the principle quantum number is the same. The correct answers are a. 1, c. 4, and d. 2
When the principle quantum number is the same, the energy of the orbitals is determined by the azimuthal quantum number (l). The azimuthal quantum number defines the shape of the orbital.
The orbitals are organized into subshells based on their azimuthal quantum number. The subshells are labeled as s, p, d, and f, with increasing values of l. The energy of the subshells increases as follows: s < p < d < f.
In this case, we are given the principle quantum number but not the azimuthal quantum number. However, we can infer the azimuthal quantum number from the given orbital numbers.
The azimuthal quantum number for the 1st orbital is 0, corresponding to an s orbital.
The azimuthal quantum number for the 5th orbital is 1, corresponding to a p orbital.
The azimuthal quantum number for the 4th orbital is 0, corresponding to an s orbital.
The azimuthal quantum number for the 2nd orbital is 0, corresponding to an s orbital.
The azimuthal quantum number for the 3rd orbital is 1, corresponding to a p orbital.
Comparing the orbitals, we can see that the s orbitals (1st, 4th, and 2nd orbitals) have lower energy than the p orbitals (5th and 3rd orbitals). Therefore, the lowest energy orbitals are the s orbitals.