Structure 1.3.3—The main energy level is given an integer number, n, and can hold a maximum of

2n^{2} electrons

**What You’ll Learn:**

- Deduce the maximum number of electrons that can occupy each energy level.

**Keywords**

Emission spectra, excited states, lower energy levels, electromagnetic spectrum, wavelength, frequency, energy, continuous spectrum, line spectrum, hydrogen emission spectrum, energy transitions, Balmer series, Lyman series, Paschen series, Rydberg formula, principal quantum number (n), maximum number of electrons, Aufbau principle, main energy level, sublevels (s, p, d, and f), atomic orbitals, s orbital, p orbitals (p_{x}, p_{y}, and p_{z}),

d orbitals (d_{xy}, d_{xz}, d_{yz}, d_{x²-y²}, and d_{z²}), orbital shapes and orientations, nodal planes, electron configuration, chemical environment, opposite spin, Aufbau principle, Hund’s rule, Pauli exclusion principle, full electron configurations, condensed electron configurations, noble gas core, orbital diagrams (arrow-in-box diagrams)

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**Syllabus Links**

Structure 3.1—How does an element’s highest main energy level relate to its period number in the periodic table?

The main energy level, also known as the principal quantum number, is given an integer number represented by the symbol n. Each energy level can hold a maximum number of electrons, which can be calculated using the formula:

Maximum number of electrons = 2n²

This formula is derived from the fact that each energy level contains a specific number of subshells (s, p, d, and f), and each subshell has a certain number of orbitals. Each orbital can hold up to two electrons with opposite spins.

Using this formula, we can deduce the maximum number of electrons that can occupy each energy level:

- First energy level (n = 1): Maximum number of electrons = 2(1)² = 2
- Second energy level (n = 2): Maximum number of electrons = 2(2)² = 8
- Third energy level (n = 3): Maximum number of electrons = 2(3)² = 18
- Fourth energy level (n = 4): Maximum number of electrons = 2(4)² = 32

And so on for higher energy levels. It is important to note that the distribution of electrons in the subshells follows the Aufbau principle, which states that electrons fill the lowest energy levels and orbitals first before occupying higher energy levels and orbitals.

Questions

- What is the principal quantum number and what does it represent?
- How is the maximum number of electrons that an energy level can hold calculated?
- What is the relationship between subshells, orbitals, and electrons in an energy level?
- How many electrons can the first four energy levels hold based on the formula?
- What is the Aufbau principle and how does it relate to the distribution of electrons in energy levels?