University Physics Volume 3

# Key Equations

### Key Equations

 Electrostatic energy for equilibrium separation distance between atoms $Ucoul=−ke2r0Ucoul=−ke2r0$ Energy change associated with ionic bonding $Uform=Etransfer+Ucoul+UexUform=Etransfer+Ucoul+Uex$ Critical magnetic field of a superconductor $Bc(T)=Bc(0)[1−(TTc)2]Bc(T)=Bc(0)[1−(TTc)2]$ Rotational energy of a diatomic molecule $Er=l(l+1)ℏ22IEr=l(l+1)ℏ22I$ Characteristic rotational energy of a molecule $E0r=ℏ22IE0r=ℏ22I$ Potential energy associated with the exclusion principle $Uex=ArnUex=Arn$ Dissociation energy of a solid $Udiss=αke2r0(1−1n)Udiss=αke2r0(1−1n)$ Moment of inertia of a diatomic molecule with reduced mass $μμ$ $I=μr02I=μr02$ Electron energy in a metal $E=π2ℏ22mL2(n12+n22+n32)E=π2ℏ22mL2(n12+n22+n32)$ Electron density of states of a metal $g(E)=πV2(8meh2)3/2E1/2g(E)=πV2(8meh2)3/2E1/2$ Fermi energy $EF=h28me(3NπV)2/3EF=h28me(3NπV)2/3$ Fermi temperature $TF=EFkBTF=EFkB$ Hall effect $VH=uBwVH=uBw$ Current versus bias voltage across p-n junction $Inet=I0(eeVb/kBT−1)Inet=I0(eeVb/kBT−1)$ Current gain $Ic=βIBIc=βIB$ Selection rule for rotational energy transitions $Δl=±1Δl=±1$ Selection rule for vibrational energy transitions $Δn=±1Δn=±1$