Key Equations

Orbital angular momentum	$L = \sqrt{l (l + 1)} ℏ$
z-component of orbital angular momentum	$L_{z} = m ℏ$
Radial probability density function	$P (r) d r = \| ψ_{n 00} \|^{2} 4 π r^{2} d r$
Spin angular momentum	$S = \sqrt{s (s + 1)} ℏ$
z-component of spin angular momentum	$S_{z} = m_{s} ℏ$
Electron spin magnetic moment	${\vec{μ}}_{s} = (\frac{e}{m_{e}}) \vec{S}$
Electron orbital magnetic dipole moment	$\vec{μ} = − (\frac{e}{2 m_{e}}) \vec{L}$
Potential energy associated with the magnetic interaction between the orbital magnetic dipole moment and an external magnetic field $\vec{B}$	$U (θ) = − μ_{z} B = m μ_{B} B$
Maximum number of electrons in a subshell of a hydrogen atom	$N = 4 l + 2$
Selection rule for atomic transitions in a hydrogen-like atom	$Δ l = \pm 1$
Moseley’s law for X-ray production	$(Z - 1) = constant \sqrt{f}$