The emission from C can be used for wavelength calibration o

The emission from C can be used for wavelength calibration of instruments in the ultraviolet. This is generally performed by electron-impact initiated decomposition of a precursor resulting in the prodiction of electronically excited C, which relaxes to the ground electronic state by emitting a photon at 193.09nm.

Suppose one wated to take another approach where C is heated until 5% of the atoms occupy the electronically excited state. Consedering only the lowest-energy ground state and the elctronically excited state, what temperature is required to achieve this excited-state population?

thanks!!!!

Solution

No/N =exp( -E/kT)/Z , given No/N = 5/100,

E = hc/lamda = 6.625 x10^ -34 x 3x10^ 8/(193.09 x10^ -9) = 1.03 x10^ -18,

Eground state = 0 ,

Z = exp(-Eo/kT) + exp(-E1/kT) = 1+exp(-1.03x10^ -18/1.38x10^ -23xT) = 1+exp(-74637.7/T)

5/100 = exp( -74637.7/T)/( 1+exp(-74637.7/T) ,

0.05(1+exp(-74637.7/T)) = exp( -74637.7/T) ,

0.05 = 0.95exp(-74637.7/T) ,

solving we get T