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Quantum numbers.

Each electron in an atom is associated with a set of four quantum numbers:

- The principal quantum number (главное квантовое число)

- The angular momentum quantum number (орбитальное квантовое число)

- The magnetic quantum number (магнитное квантовое число)

- The spin projection quantum number (спиновое квантовое число).

Example: The quantum numbers used to refer to the outermost valence electrons of the Carbon (C) atom, which are located in the 2p atomic orbital, are; n = 2 (2nd electron shell), ℓ = 1 (p orbital subshell), m_ℓ = 1, 0 or −1, m_s = ½ (parallel spins).

The principal quantum number (n) can have any positive integral value, but the electrons in atoms in their most stable states have principal quantum numbers with values from 1 through 7 only. The most stable electronic state of an atom is called its ground state. Any higher energy state is called an excited state. (Unless “excited state” is specified in later discussions, ground state is implied.)

The principal quantum number has the largest role in determining the energy of the electron, and it is also the main factor in determining how far the electron is, on average, from the nucleus. Thus, it is the most important quantum number.

For each value of n, the angular momentum quantum number (l) for an electron can have integral values from zero to (n-1) it cannot be as large as n. The angular momentum quantum number has a small role in determining the energy of the electron, and it determines the shape of the volume of space that the electron can occupy.

For each value of the angular momentum quantum number (l) the magnetic quantum number (m_l) has values ranging from -l through zero to +l in integral steps. The value of m_l does not ordinarily affect the energy of an electron, but it does determine the orientation in space of the volume that can contain the electron.

The spin quantum number (m_s) may have values of -1/2 or +1/2 only. The value of does not depend on the value of any other quantum number. The spin value gives the orientation of the magnetic field associated with the electron.

Another important limitation on the quantum numbers of electrons in atoms, is the Pauli exclusion principle. This principle states that no two electrons in an atom can have the same set of four quantum numbers. This is like the business law that states that no two tickets to a rock concert can have the same set of date and section, row, and seat numbers. The row number may depend on the section number, and the seat number may depend on the row number, but the date does not depend on any of the other three. Similarly, the spin quantum number is independent of the other three quantum numbers.

Hund’s rule states that the electrons within a given subshell remain as unpaired as possible. Or, the lowest energy configuration for an atom is the one having the maximum number of unpaired electrons allowed by the Pauli principle in a particular set of degenerate orbitals. Moreover, if there are two or more unpaired electrons ina given subshell, they all must occupy different orbitals and have the sameelectron spin (all arrows representing unpaired electrons in a subshell point upor all point down). The energy level diagrams for the carbon, nitrogen, andoxygen atoms illustrate these rules: