A hypothetical atom has only two atomic energy levels, separated by 3.2 eV. Suppose that at a certain altitude in the atmosphere of a star there are `6.1xx10^(13)//cm^(3)` of these atoms in the higher-energy state and are `2.2xx10^(15)//cm^(3)` in the lower-energy state. What is the temperature of the star's atmosphere at that altitude?

Explanation

To find the temperature of the star's atmosphere at a certain altitude given the number of atoms in two energy states, we can use the Boltzmann distribution. Here’s a step-by-step solution:

### Step 1: Identify the Given Values
- Energy difference between the two levels, ΔE = 3.2 eV
- Number of atoms in the higher energy state, n_high = \(6.1 \times 10^{13} \, \text{cm}^{-3}\)
- Number of atoms in the lower energy state, n_low = \(2.2 \times 10^{15} \, \text{cm}^{-3}\)

### Step 2: Use the Boltzmann Distribution Formula
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