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Cold interstellar molecular clouds often contain the
Chapter 6, Problem 12P(choose chapter or problem)
Cold interstellar molecular clouds often contain the molecule cyanogen (CN), whose first rotational excited states have an energy of \(4.7 \times 10^{-4} \mathrm{eV}\) (above the ground state). There are actually three such excited states, all with the same energy. In 1941, studies of the absorption spectrum of starlight that passes through these molecular clouds showed that for every ten CN molecules that are in the ground state, approximately three others are in the three first excited states (that is, an average of one in each of these states). To account for this data, astronomers suggested that the molecules might be in thermal equilibrium with some “reservoir” with a well-defined temperature. What is that temperature?
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QUESTION:
Cold interstellar molecular clouds often contain the molecule cyanogen (CN), whose first rotational excited states have an energy of \(4.7 \times 10^{-4} \mathrm{eV}\) (above the ground state). There are actually three such excited states, all with the same energy. In 1941, studies of the absorption spectrum of starlight that passes through these molecular clouds showed that for every ten CN molecules that are in the ground state, approximately three others are in the three first excited states (that is, an average of one in each of these states). To account for this data, astronomers suggested that the molecules might be in thermal equilibrium with some “reservoir” with a well-defined temperature. What is that temperature?
ANSWER:Step 1 of 4
Consider \(E_{1}\) be the ground state energy and \(E_{2}\) be the first excited state energy so the probability is given by,
\(\mathcal{P}(s)=\frac{1}{Z} e^{-E / k T}\)
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