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The principal quantum number was first created for use in the semiclassical Bohr model of the atom, distinguishing between different energy levels. With the development of modern quantum mechanics, the simple Bohr model was replaced with a more complex theory of atomic orbitals .
For example, the "4s subshell" is a subshell of the fourth (N) shell, with the type (s) described in the first row. The second column is the azimuthal quantum number (ℓ) of the subshell. The precise definition involves quantum mechanics, but it is a number that characterizes the subshell.
Four quantum numbers can describe an electron energy level in a hydrogen-like atom completely: Principal quantum number (n) Azimuthal quantum number (ℓ) Magnetic quantum number (m ℓ) Spin quantum number (m s) These quantum numbers are also used in the classical description of nuclear particle states (e.g. protons and neutrons).
If the group is of the [ns, np] type, an amount of 0.85 from each electron with principal quantum number (n–1), and an amount of 1.00 for each electron with principal quantum number (n–2) or less. If the group is of the [d] or [f], type, an amount of 1.00 for each electron "closer" to the nucleus than the group.
An electron shell is the set of allowed states that share the same principal quantum number, n, that electrons may occupy. In each term of an electron configuration, n is the positive integer that precedes each orbital letter (helium's electron configuration is 1s 2, therefore n = 1, and the orbital contains two electrons).
The maximum number of electrons in any shell is 2n 2, where n is the principal quantum number. The maximum number of electrons in a subshell is equal to 2(2 l + 1), where the azimuthal quantum number l is equal to 0, 1, 2, and 3 for s, p, d, and f subshells, so that the maximum numbers of electrons are 2, 6, 10, and 14 respectively.
The number of nodal spheres equals n-ℓ-1, consistent with the restriction ℓ ≤ n-1 on the quantum numbers. The principal quantum number controls the total number of nodal surfaces which is n-1. [31] Loosely speaking, n is energy, ℓ is analogous to eccentricity, and m is orientation.
9/2: [7] Terms are assigned for each group (with different principal quantum number n) and rightmost level 6 F o 9/2 is from coupling of terms of these groups so 6 F o 9/2 represents final total spin quantum number S, total orbital angular momentum quantum number L and total angular momentum quantum number J in this atomic energy