Electrons exist in specific, quantized main energy levels (n). They cannot exist between levels.
Key Principles
- 1Energy Increases with n: n=1 is closest to the nucleus (Ground State) and has the lowest energy. High n = High Energy.
- 2Convergence: As n increases, the energy gaps between shells get smaller. The levels "converge" at \(n = \infty \).
Energy Increases ↑
Gap Decreases
n=1 (Ground)
n=2
UV Photon
n=3
n=4
n=5
n=∞ (Convergence)
Hover over levels to see precision. Note the "Convergence Limit" at the top.
Maximum Electrons per Shell
\(2n^2\)
Shell n=1
2
Shell n=2
8
Shell n=3
18
Shell n=4
32
Deep Think Concept
Why do shells converge?
The attraction from the nucleus drops off with distance (Inverse Square Law). At higher energy levels (further away), the difference in attraction between step n and step n+1 becomes negligible, so the energy difference (\(\Delta E\)) becomes tiny.
Student Practice Set
1.
What is the maximum number of electrons in the 3rd main energy level (n=3)?
2.
Which transition emits the highest energy photon?