What is the maximum number of electrons in an atom whose highest-energy electrons have the principal quantum number n = 5?

검증된 단계별 안내

Identify the principal quantum number n = 5, which indicates the fifth energy level.

Recall that the maximum number of electrons in an energy level is given by the formula 2n^2.

Substitute n = 5 into the formula to calculate the maximum number of electrons: 2(5)^2.

Simplify the expression to find the maximum number of electrons in the fifth energy level.

Conclude that this is the maximum number of electrons that can occupy the fifth energy level in an atom.

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Principal Quantum Number (n)

The principal quantum number, denoted as 'n', indicates the energy level of an electron in an atom. It can take positive integer values (1, 2, 3, ...), with higher values corresponding to electrons that are further from the nucleus and have higher energy. For n = 5, the electrons are in the fifth energy level.

Electron Capacity of Energy Levels

Each principal energy level can hold a maximum number of electrons determined by the formula 2n², where 'n' is the principal quantum number. For n = 5, the maximum number of electrons is calculated as 2(5)² = 50. This capacity reflects the arrangement of electrons in various sublevels and orbitals within that energy level.

Sublevels and Orbitals

Energy levels are divided into sublevels (s, p, d, f), which contain orbitals where electrons reside. Each sublevel has a specific number of orbitals: s has 1, p has 3, d has 5, and f has 7. The distribution of electrons among these sublevels influences the chemical properties of the atom, but the total number of electrons is still limited by the maximum capacity of the principal energy level.