Atomic Structure

The Bohr model, proposed by Niels Bohr in 1913, describes the atom as a small, positively charged nucleus orbited by electrons in fixed, circular paths called energy levels or shells. Electrons can only exist in these specific energy levels and do not radiate energy while in them. Electrons can move between energy levels by absorbing or emitting discrete quanta of energy (photons). This model successfully explained the line spectrum of hydrogen but failed for multi-electron atoms and could not explain the fine structure of spectral lines or the Zeeman effect.

Quantum numbers are a set of four numbers that describe the unique state of an electron in an atom, including its energy, shape of its orbital, and spatial orientation. They arise from the mathematical solutions to the Schrödinger wave equation.

The principal quantum number (n) describes the main energy level or shell in which an electron resides. It determines the electron's energy and the average distance of the electron from the nucleus. Higher values of 'n' correspond to higher energy levels and larger orbitals. 'n' can take positive integer values: 1, 2, 3, ...

The azimuthal or angular momentum quantum number (l) describes the shape of an electron's orbital and defines the sub-shell within a given main energy level. Its value depends on 'n' and can range from 0 to (n-1). Each 'l' value corresponds to a specific sub-shell type: l=0 for s-sub-shell, l=1 for p-sub-shell, l=2 for d-sub-shell, and l=3 for f-sub-shell.

The magnetic quantum number (ml) describes the orientation of an orbital in space. Its value depends on 'l' and can range from -l through 0 to +l. For a given 'l', there are (2l+1) possible 'ml' values, which correspond to the number of orbitals within that sub-shell.

The spin quantum number (ms) describes the intrinsic angular momentum of an electron, often referred to as its 'spin'. Electrons behave as if they are spinning, creating a magnetic field. There are only two possible spin orientations, represented by +1/2 (spin up) and -1/2 (spin down).

Sub-shells are groups of orbitals within a main energy level that have the same shape. They are defined by the azimuthal quantum number (l).

The s-sub-shell contains one orbital (ml=0). All s-orbitals are spherical in shape. Each s-orbital can hold a maximum of 2 electrons.

The p-sub-shell contains three orbitals (ml=-1, 0, +1). These orbitals are dumbbell-shaped and are oriented along the x, y, and z axes (px, py, pz). Each p-sub-shell can hold a maximum of 6 electrons (2 electrons per orbital x 3 orbitals).

The d-sub-shell contains five orbitals (ml=-2, -1, 0, +1, +2). These orbitals have more complex shapes, typically cloverleaf-shaped. Each d-sub-shell can hold a maximum of 10 electrons (2 electrons per orbital x 5 orbitals).

The f-sub-shell contains seven orbitals (ml=-3, -2, -1, 0, +1, +2, +3). These orbitals have even more complex shapes. Each f-sub-shell can hold a maximum of 14 electrons (2 electrons per orbital x 7 orbitals).

Electronic configuration describes the distribution of electrons among the atomic orbitals of an atom or ion. It follows three main rules:

The Aufbau principle states that electrons fill atomic orbitals in order of increasing energy. Lower energy orbitals are filled before higher energy orbitals. The general order is 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p, 7s, 5f, 6d, 7p.

Hund's rule states that for degenerate orbitals (orbitals of the same energy, e.g., the three p-orbitals), electrons will occupy each orbital singly with parallel spins before any orbital is doubly occupied.

The Pauli exclusion principle states that no two electrons in an atom can have the same set of four quantum numbers (n, l, ml, ms). This means that an atomic orbital can hold a maximum of two electrons, and these two electrons must have opposite spins.