Question

For Mg+ ion, calculate the ratios of the number of ions in the 3p excited state to the number in the ground state in a heat source with temperature of (a) Temperature of 7250 K (b) Temperature of 1800 K The wavelength of the photon emitted from a Mg+ ion in the 3p excited state is 280 nm when it transfers to ground state.

Answer 1

In this case, at those temperatures, we'll do it in two parts.

a) at 7250 K

Pj/Po = 6/2

First we calculate the Energy (This energy will be the same for the second part)

= hc / h = 6.63x10^-34 J s; c = 3x10⁸ m/s; = 280x10^-9 m

= 6.63x10^-34 * 3x10⁸ / 280x10^-9 = 7.1x10^-19 J

Nj/No = Pj/Po exp(-/kT) k = 1.38x10^-23 J/K

Nj/No = 6/2 exp(-7.1x10^-19 / 1.38x10^-23 * 7250)

Nj/No = 2.48x10^-3

b) at 1800 K

Nj/No = 6/2 exp(-7.1x10^-19 / 1.38x10^-23 * 1800)

Nj/No = 1.16x10^-12

Hope this helps