Final answer:
The question relates to finding the temperature at which the relative population of hydrogen atoms in the first excited state is 1% and 10% of those in the ground state, using Bohr's hydrogen atom model and the Boltzmann distribution formula.
Step-by-step explanation:
The student's question is related to Bohr's theory of the hydrogen atom and utilizes the concept of relative population and energy levels to determine the temperature at which the number of atoms in the first excited state is a certain percentage of the number in the ground state. According to the Boltzmann distribution, the population ratio of atoms in two energy states at a given temperature is given by:
P(n) = Ce-en/kT
where P(n) is the population of the excited state, C is a normalization constant, e is the energy difference between the two states, n is the quantum number, k is the Boltzmann constant, and T is the temperature in Kelvin.
For hydrogen, the energy difference (e) between the ground state (n=1) and the first excited state (n=2) is known. Thus, we can set up an equation where the population of the first excited state, P(2), is 1% or 10% of the population of the ground state, P(1), and solve for T to find the corresponding temperatures for parts a and b.