Key Equations

Key Equations

Orbital angular momentum	$L=\sqrt{l(l+1)}\hslash$
z-component of orbital angular momentum	$L_z=m\hslash$
Radial probability density function	$P(r)dr=|{\psi }_{n00}{|}^{2}4\pi r^{2}dr$
Spin angular momentum	$S=\sqrt{s(s+1)}\hslash$
z-component of spin angular momentum	$S_z=m_s\hslash$
Electron spin magnetic moment	${\overrightarrow{\mathit{\text{μ}}}}_s=\left(\frac{e}{m_e}\right)\overrightarrow{S}$
Electron orbital magnetic dipole moment	$\overrightarrow{\mathit{\text{μ}}}=\text{−}\left(\frac{e}{2m_e}\right)\overrightarrow{L}$
Potential energy associated with the magnetic interaction between the orbital magnetic dipole moment and an external magnetic field $\overrightarrow{B}$	$U\left(\theta \right)=\text{−}{\mu }_{z}B=m{\mu }_{\text{B}}B$
Maximum number of electrons in a subshell of a hydrogen atom	$N=4l+2$
Selection rule for atomic transitions in a hydrogen-like atom	$\text{Δ}l=\pm 1$
Moseley’s law for X-ray production	$\left(Z-1\right)=\text{constant}\sqrt{f}$