原子空孔

${\displaystyle F=U-TS}$

${\displaystyle U=nE}$

${\displaystyle S=kln(\omega )}$

${\displaystyle \omega ={\frac {(N+n)!}{N!n!}}}$

${\displaystyle S=k\ln({\frac {(N+n)!}{N!n!}})}$

${\displaystyle S=k\{(N+n)\ln(N+n)-N\ln(N)-n\ln(n)\}}$

${\displaystyle S=k\{(N+n)\ln(N+n)-N\ln(N)-n\ln(n)\}+S'}$

${\displaystyle {\frac {dF}{dn}}=E-T\{S'+k\ln(N+n)-k\ln(n)\}=0}$

${\displaystyle {\frac {n}{N+n}}=\exp({\frac {S'}{k}})\times \exp({\frac {-E}{kT}})}$

${\displaystyle c={\frac {n}{N}}=\exp({\frac {S'}{k}})\times \exp({\frac {-E}{kT}})}$