Quantum Theory of the Atom

A quantum number representing the energy level of an electron in an atom.

A quantum number describing the shape of an electron's orbital.

A quantum number describing the orientation of an electron's orbital in space.

A quantum number describing the intrinsic angular momentum of an electron, known as spin.

A region in space around the nucleus of an atom where an electron is most likely to be found.

The set of quantum numbers that describe the state of an electron in an atom.

The energy level of an electron is primarily determined by its principal quantum number (n). However, the energy can also be influenced by the angular momentum quantum number (l), with higher values of l indicating slightly higher energy levels.

A subshell within a particular shell is denoted by the value of the principal quantum number (n) followed by the letter designation for the subshell (e.g., 2p represents a subshell with n = 2 and l = 1).

The magnetic quantum number (ml) describes the spatial orientation of an atomic orbital within a subshell and determines the number of orbitals within that subshell.

The value of ml can range from -l to +l, including 0. For example, if l = 1, ml can be -1, 0, or +1, resulting in three orbitals.

Each value of ml corresponds to a specific orbital within a subshell. For example, a p subshell (l = 1) has three orbitals (ml = -1, 0, +1).

The total number of orbitals in a subshell is 2l+1. For example, a d subshell (l=2) has 5 orbitals (2 * 2 + 1).

The electron spin quantum number (ms) describes the intrinsic angular momentum of an electron, which is quantized and referred to as spin angular momentum. Since it's a property related to the inherent spin of an electron, it's independent of its orbital motion.

The electron spin can be either spin up (ms = +1/2) or spin down (ms = -1/2).

Each subshell has a specific number of orbitals, each with a unique shape and energy.

• s subshells have 1 orbital
• p subshells have 3 orbitals
• d subshells have 5 orbitals
• f subshells have 7 orbitals

Each subshell contains one or more orbitals, each with a distinct shape and energy level. For example, the s subshell contains a spherical orbital, while the p subshell contains three dumbbell-shaped orbitals. The shape and orientation of orbitals contribute to the overall energy of an electron within an atom.