Final answer:
To find the population ratios of the three lowest levels in hydrogen at a temperature of 5000 K, we can use the Boltzmann distribution law. This law states that the population ratio of two energy levels is directly proportional to the ratio of their respective energies.
Step-by-step explanation:
The population ratios of the three lowest levels in hydrogen at a temperature of 5000 K can be determined using the Boltzmann distribution law. According to the law, the population ratio of two energy levels is directly proportional to the ratio of their respective energies.
Let's consider the energy levels n=1, n=2, and n=3 for hydrogen. The energy of these levels can be calculated using the formula:
E = -13.6 eV / n^2
Substituting n=1, n=2, and n=3 into the formula, we can find the corresponding energies. Then, we can calculate the population ratios by dividing the Boltzmann factors, which are given by:
p_n/p_1 = e^(-E_n/kT)
where p_n is the population of level n, p_1 is the population of the lowest level (n=1), E_n is the energy of level n, k is the Boltzmann constant (8.617 × 10^-5 eV/K), and T is the temperature in Kelvin.