Question

A population inversion for two energy levels is often described by assigning a negative Kelvin temperature to the system. What negative temperature would describe a system in which population of the upper energy level exceeds that of the lower by `10%` and the energy difference between the two levels is 2.2 eV?

Answer 1

As `N_(x)=N_(0)e^(-(E_(x)-E_(0))//kT) :. (N_(x))/(N_(0))e^(-(E_(x)-E_(0))//kT)`
`ln ((N_(x))/(N_(0)))=-(E_(x)-E_(0))/(kT)` or `-T=(E_(x)-E_(0))/(k ln((N_(x))/(N_(0))))`
Now, `E_(x)-E_(0)=2.2eV and (N_(x))/(N_(0))=1.10, k=8.62xx10^(-5)eV//K`
`:. -T=(2.2eV)/((8.62xx10^(-5)eV//K)ln(1.10))=2.67xx10^(5)K or T=-2.67xx10^(5)K`