Find relative number of H atoms in n=1,2,3,4 energy levels

• xatu
In summary, the problem is to find the relative numbers of hydrogen atoms in the chromosphere at different energy levels, and the solution involves using the Boltzmann distribution of energies with calculated ratios of 1 : 5.4 x 10^-11 : 6.7 x 10^-13 : 1.5 x 10^-13. However, this formula may not be applicable to this problem as it deals with a system with discrete energies.
xatu
The problem:

Find the relative numbers of hydrogen atoms in the chromosphere (T=5000 K) in the n=1, 2, 3, and 4 energy levels.

Solution:

The Boltzmann distribution of energies is

$n(ε)dε=\frac{2πN}{(πkT)^{3/2}}\sqrt{ε}e^{-ε/kT}dε$

So using this I calculated the ratio to be, 1 : 5.4 x 10^-11 : 6.7 x 10^-13 : 1.5 x 10^-13.

Can anyone confirm this?

xatu said:
The Boltzmann distribution of energies is

$n(ε)dε=\frac{2πN}{(πkT)^{3/2}}\sqrt{ε}e^{-ε/kT}dε$

This is not applicable to this problem. You are dealing with a system that has discrete energies. See http://en.wikipedia.org/wiki/Boltzmann_distribution

Actually I used that formula, accounting for the degeneracies of the energy levels, and got the correct answer.

Last edited:

1. How many energy levels are there in the n=1,2,3,4 series?

The n=1,2,3,4 series has a total of 4 energy levels.

2. What is the maximum number of H atoms that can be found in each energy level?

The maximum number of H atoms that can be found in each energy level is given by the formula 2n^2, where n is the energy level number. Therefore, for n=1, there can be a maximum of 2(1)^2 = 2 H atoms; for n=2, there can be a maximum of 2(2)^2 = 8 H atoms; for n=3, there can be a maximum of 2(3)^2 = 18 H atoms; and for n=4, there can be a maximum of 2(4)^2 = 32 H atoms.

3. How many total H atoms can be found in the n=1,2,3,4 energy levels?

The total number of H atoms in the n=1,2,3,4 energy levels is calculated by adding up the maximum number of H atoms in each energy level. Therefore, the total number of H atoms is 2 + 8 + 18 + 32 = 60.

4. How does the number of H atoms in each energy level change as n increases?

The number of H atoms in each energy level increases as n increases. This is because the formula for the maximum number of H atoms (2n^2) increases as n increases. Therefore, as n increases, the number of H atoms also increases.

5. Is there a limit to the number of energy levels and H atoms in the n=1,2,3,4 series?

Yes, there is a limit to the number of energy levels and H atoms in the n=1,2,3,4 series. As n approaches infinity, the number of energy levels and H atoms also approaches infinity. However, in practical terms, the maximum number of energy levels and H atoms that can be observed and studied is limited by technological and scientific capabilities.

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