The relative energies of the sublevels within the principal energy levels are 1lt 3lt 5lt 7 slt plt dlt f 1lt 2lt 3lt 4 flt dlt plt s

The correct answer describing the relative energies of sublevels within principal energy levels is **none of the provided options**. The options given present pieces of the puzzle but don't accurately reflect how sublevel energies relate, especially in atoms beyond hydrogen.<br /><br />Here's a breakdown of why the given options are incorrect and what the correct principle is:<br /><br />* **Option 1: `1 < 3 < 5 < 7` and Option 3: `1 < 2 < 3 < 4`**: These refer to principal quantum numbers (n). While it's true that higher principal quantum numbers generally correspond to higher energy levels, this doesn't tell the whole story about sublevel energies *within* those levels.<br /><br />* **Option 2: `s < p < d < f` and Option 4: `f < d < p < s`**: These refer to the azimuthal quantum number (l) which defines the sublevels (s, p, d, f). While within a *given* principal energy level (like n=2), it's generally true that s < p < d < f in energy, this order doesn't hold across different principal energy levels.<br /><br />**The Correct Principle: The Aufbau Principle and Madelung's Rule**<br /><br />The filling of atomic orbitals follows the Aufbau principle, which states that electrons fill atomic orbitals of the lowest available energy levels before occupying higher levels. A useful tool for predicting this order is Madelung's rule (with some exceptions):<br /><br />Orbitals are filled in order of increasing *n + l* values. For orbitals with the same *n + l* value, the one with the lower *n* value fills first.<br /><br />This leads to the following order (up to 6p, which is generally sufficient for most chemistry):<br /><br />1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p, ...<br /><br />Notice how the 4s orbital fills *before* the 3d orbitals, and similarly, the 5s fills before the 4d. This overlapping of energy levels is what makes the simple ordering in the provided options incorrect.<br />