P

Principal Quantum Number

n = 1,2,3...; E_n = −13.6/n² eV (H)
Quick Reference
Formula / Notationn = 1,2,3...; E_n = −13.6/n² eV (H)
Also Known AsPrincipal quantum number n, shell number, energy quantum number

What is Principal Quantum Number?

The quantum number (n) that determines the energy level and size of an atomic orbital. Takes positive integer values (1, 2, 3...). Higher n values correspond to orbitals farther from the nucleus with higher energy. The principal quantum number is the most important factor in determining electron energy.

Formula & Notation

n = 1,2,3...; E_n = −13.6/n² eV (H)

Other Names / Synonyms: Principal quantum number n, shell number, energy quantum number

Properties & Characteristics

The principal quantum number (n) is the primary quantum number describing the electron's energy level and the size of the orbital in an atom. It takes positive integer values (n = 1, 2, 3, ...). For hydrogen: energy E_n = −13.6/n² eV (negative because bound). For polyelectronic atoms, the energy depends on both n and l (subshell). The principal quantum number determines the shell: n=1 (K shell), n=2 (L shell), n=3 (M shell), etc. Maximum electrons per shell: 2n².

Uses & Applications

The principal quantum number determines the energy and size of orbitals, explains the emission spectrum of hydrogen (Balmer, Lyman, Paschen series correspond to transitions to n=2, n=1, n=3 respectively), governs the number of subshells and orbitals per shell (n subshells, n² orbitals per shell), and is the basis for organising the periodic table into periods.

Safety Information

No direct safety concern. Understanding principal quantum numbers helps explain why outer-shell (large n) electrons are more easily ionised (farther from nucleus, less bound), making large-n elements in Group 1 more reactive and more hazardous toward water and air.

Always consult the SDS/MSDS before handling any chemical. This information is for educational purposes only.

Key Facts

Term Principal Quantum Number
Formula n = 1,2,3...; E_n = −13.6/n² eV (H)
Synonyms Principal quantum number n, shell number, energy quantum number

Frequently Asked Questions

The quantum number (n) that determines the energy level and size of an atomic orbital. Takes positive integer values (1, 2, 3...). Higher n values correspond to orbitals farther from the nucleus with higher energy. The principal quantum number is the most important factor in determining electron energy.

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