Quantum numbers

[Jolene Robles 2H]

Hello,

I am confused on how you match up quantum numbers with the 4 orbitals. For example, how do you know which specific sub shell will accommodate an electron with a certain set of quantum numbers?

[isabella hawthorne 3B]

To determine which specific subshell will accommodate an electron with a certain set of quantum numbers, you need to consider the values of the principal quantum number, azimuthal quantum number and magnetic quantum number. The quantum numbers play a role in describing the electron configuration of an atom, and they provide a way of characterizing the distribution of electrons in the atomic orbitals. The principal quantum number (n) describes the energy level or shell of an electron in an atom. Larger values of n indicate higher energy levels, and each energy level can contain one or more subshells. The azimuthal quantum number (l) specifies the shape of the orbital within a given energy level. The magnetic quantum number (m_l) defines the orientation of the orbital in space. For a given subshell (specified by l), the values of m_l range from -l to +l, including zero. The spin quantum number (m_s) describes the intrinsic spin of an electron.

[Levy Shaked]

Agreed. More specifically with respect to your question, the linear momentum quantum number, l, specifies the subshell that the electron will be located in. l=0 corresponds to the s orbital, l=1 corresponds to the p orbitals, l=2 corresponds to the d orbitals, and l=3 corresponds to the f orbitals. For a given principle quantum number n, the possibilities for l range from 0 to n-1. This means that, while electrons in atoms of the first period can only be found in the s orbital, electrons in the second period can be s or p; electrons in the third period can be s, p, or d (although ground-state electrons are not found in d orbitals until the fourth period as 4s orbitals are lower energy than 3d orbitals); and electrons in the fourth period can be s, p, d or f (although ground-state electrons are not found in f orbitals until the sixth period, as 5s, 4d, 5p and 6s orbitals are lower energy than 4f orbitals). Electrons will always occupy the lowest-energy orbital available to them, but for an individual electron's specific set of quantum numbers, its value for l directly corresponds to the subshell it occupies.