Final answer:
The relative population of sodium atoms in excited vs ground state can be found using the Boltzmann distribution, which involves the energy difference between states and the temperature. By inputting the given energy levels, degeneracies, and temperatures for the flame (3000 K) and plasma (10,000 K), we can calculate the ratios of populations for each source.
Step-by-step explanation:
The relative population of sodium atoms in the excited state compared to the ground state can be determined using the Boltzmann distribution. The Boltzmann distribution relates the probability of an atom being in a particular energy state at a given temperature. The probability P(n) of an atom being in the energy level n is given by:
P(n) = Ce-εn/kT
where C is a normalization constant, εn is the energy of level n, k is Boltzmann's constant, and T is the temperature in kelvins. Since we're interested in the relative population between the excited state (n=1) and ground state (n=0), we can set the ratio:
P(1)/P(0) = (g₁/g₀)e-(E₁-E₀)/kT
where g₀ and g₁ are the degeneracies of the ground and first excited states, respectively, and E₁-E₀ is the energy difference between these states. Given that E₀ = 3.371x10-19 J, g₀ = 1, g₁ = 2, and the temperatures for our flame and plasma sources are 3000 K and 10,000 K respectively, the relative populations can be calculated for each source.
For example, for the flame source at 3000 K:
P(1)/P(0) = (2/1)e-(3.371x10-19)/(1.38x10-23x3000)
This calculation can be repeated for the plasma source at 10,000 K to find the relative populations in that case.