Based on the analysis of the provided image, here is the solution and explanation.
The image displays a diagram known as the
Aufbau principle diagram or the
diagonal rule. This diagram illustrates the order in which atomic orbitals are filled with electrons as the atomic number (number of protons) increases across the periodic table.
The Aufbau Principle
The Aufbau principle states that electrons fill atomic orbitals of the lowest available energy levels before occupying higher levels. In other words, orbitals are filled in order of increasing energy.
How to Read the Diagram
The diagram is organized into diagonal rows. To determine the correct filling order, you follow the arrows from top to bottom and left to right along these diagonals.
1.
Start at the Top-Left: The first orbital to be filled is `1s²`.
2.
Follow the Diagonals: The arrows indicate the sequence.
* After `1s²`, you move down to `2s²`.
* Then, you follow the diagonal to `2p⁶`.
* Next, you go down to `3s²`, then diagonally to `3p⁶`.
* The next diagonal starts with `4s²`, then goes to `3d¹⁰`, and finally to `4p⁶`.
This pattern continues throughout the entire diagram, showing the complete sequence up to the `7f` orbitals.
The Underlying Rule: The n + l Rule
The order shown in the diagram is determined by the
n + l rule, where:
* `n` is the principal quantum number (the shell number).
* `l` is the azimuthal quantum number (which defines the subshell: s=0, p=1, d=2, f=3).
Orbitals are filled in order of increasing `n + l`. If two orbitals have the same `n + l` value, the one with the lower `n` value is filled first.
Let's verify this with a few examples from the diagram:
* `4s` vs. `3d`: For `4s`, `n + l = 4 + 0 = 4`. For `3d`, `n + l = 3 + 2 = 5`. Since 4 < 5, `4s` is filled before `3d`.
* `5s` vs. `4d`: For `5s`, `n + l = 5 + 0 = 5`. For `4d`, `n + l = 4 + 2 = 6`. Since 5 < 6, `5s` is filled before `4d`.
* `6s` vs. `4f`: For `6s`, `n + l = 6 + 0 = 6`. For `4f`, `n + l = 4 + 3 = 7`. Since 6 < 7, `6s` is filled before `4f`.
The Complete Filling Order
Following the arrows in the diagram, the complete order for filling orbitals is:
`1s² → 2s² → 2p⁶ → 3s² → 3p⁶ → 4s² → 3d¹⁰ → 4p⁶ → 5s² → 4d¹⁰ → 5p⁶ → 6s² → 4f¹⁴ → 5d¹⁰ → 6p⁶ → 7s² → 5f¹⁴ → 6d¹⁰ → 7p⁶`
In summary, the image provides a visual mnemonic for the Aufbau principle, allowing you to predict the electron configuration of any element by following the diagonal arrows from the top-left to the bottom-right.
Parent Tip: Review the logic above to help your child master the concept of atomic orbitals worksheet.
