Question

Mg+ ions emit a doublet (2929 nm, 2936 nm) when undergoing 4s->3p transition and another doublet (2803 nm, 2796 nm) when undergoing a 3p->3s transition. Calculate the ratio of the number of Mg(+) ions in the 4s excited state to the number of ions in the ground state in the arc cor of a DCP source (~8000k). Use the average wavelengths for transitions in your calculations.

Answer 1

The average = 2929 + 2936 /2 = 2932.5

so energy of exited state will be

E = hc/lambda = (6.62e-34 J s X 3.00e+8 m/s) / (2932.5 * 10e-9 m/nm) = 6.7 X 10^-20 J

Average = 2803+2796 / 2 = 2799.5

E = hc/l = (6.62e-34 J s * 3.00e+8 m/s) / (2799.5 * 10e-9 m/nm) = 7.09 X 10-20 J

Total energy difference between 4s and 3s =( 6.7 + 7.09 ) X 10^-20 = 13.79 X 10^-20 J

The ratio will be

N4s/N3s = 3 exp[(13.79 X 10^-20 J)/(1.38e-23 J/K X 8000K)] = 3X exp (1.24) =10.35