Key Equations

Key Equations

Electrostatic energy for equilibrium separation distance between atoms	$U_{\text{coul}}=-\frac{k{e}^2}{r_0}$
Energy change associated with ionic bonding	$U_{\text{form}}=E_{\text{transfer}}+U_{\text{coul}}+U_{\text{ex}}$
Critical magnetic field of a superconductor	$B_{\text{c}}\left(T\right)=B_{\text{c}}\left(0\right)\left[1-{\left(\frac{T}{T_{\text{c}}}\right)}^2\right]$
Rotational energy of a diatomic molecule	$E_r=l\left(l+1\right)\frac{{\hslash }^2}{2I}$
Characteristic rotational energy of a molecule	$E_{0r}=\frac{{\hslash }^2}{2I}$
Potential energy associated with the exclusion principle	$U_{\text{ex}}=\frac{A}{r^n}$
Dissociation energy of a solid	$U_{\text{diss}}=\alpha \frac{k{e}^2}{r_0}\left(1-\frac{1}{n}\right)$
Moment of inertia of a diatomic molecule with reduced mass $\mu$	$I=\mu r_0^2$
Electron energy in a metal	$E=\frac{{\pi }^2{\hslash }^2}{2m{L}^2}\left(n_1^2+n_2^2+n_3^2\right)$
Electron density of states of a metal	$g\left(E\right)=\frac{\pi V}{2}{\left(\frac{8m_e}{h^2}\right)}^{3\text{/}2}{E}^{1\text{/}2}$
Fermi energy	$E_{\text{F}}=\frac{h^2}{8m_e}{\left(\frac{3N}{\pi V}\right)}^{2\text{/}3}$
Fermi temperature	$T_{\text{F}}=\frac{E_{\text{F}}}{k_{\text{B}}}$
Hall effect	$V_{\text{H}}=uBw$
Current versus bias voltage across p-n junction	$I_{\text{net}}=I_0\left(e^{e{V}_b\text{/}{k}_{\text{B}}T}-1\right)$
Current gain	$I_c=\beta I_B$
Selection rule for rotational energy transitions	$\text{Δ}l=\pm 1$
Selection rule for vibrational energy transitions	$\text{Δ}n=\pm 1$