## Atomic Orbitals Mathematical solution to an electron wave equation describing the volume of space where an electron is most likely to be found They are described by four quantum numbers: 1. Principle, shell ($n$): orbital energy and size 2. Azimuthal, subshell ($l$): orbital shape ($s, p, d, f$) 3. Magnetic ($m_{l}$): orbital direction (${} p_{x}$, $p_{y}$, $p_{z}$) 4. Spin ($m_{s}$): +1/2 or -1/2 **Aufbau Principle**: Lowest energy orbitals fill up first: 1s, 2s, 2p, 3s, 3p, 4s, 3d, etc ![[Pasted image 20260915124607.png|414]] ### Orbital Types - *s* orbitals - electrons held close to nucleus, one sign -