The energy of the vibrational modes of a molecule are the same as those of a (quantum) harmonic oscillator with frequency w. There is a gas of nitrogen molecules in thermodynamic equilibrium for which ħw/ks-3340 K. You may approximate the vibrational partition function with the argest two terms in it. a) What fraction of the molecules are in the ground state and what fraction in the 1st excited state of their vibrational modes at a temperature of 700 K, b) At what temperature will 5% of the molecules be in the 1st excited vibrational state?
The energy of the vibrational modes of a molecule are the same as those of a (quantum) harmonic oscillator with frequency w. There is a gas of nitrogen molecules in thermodynamic equilibrium for which ħw/ks-3340 K. You may approximate the vibrational partition function with the argest two terms in it. a) What fraction of the molecules are in the ground state and what fraction in the 1st excited state of their vibrational modes at a temperature of 700 K, b) At what temperature will 5% of the molecules be in the 1st excited vibrational state?
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Transcribed Image Text:The energy of the vibrational modes of a molecule are the same as those of a (quantum)
harmonic oscillator with frequency w. There is a gas of nitrogen molecules in thermodynamic
equilibrium for which ħw/ks-3340 K. You may approximate the vibrational partition function with the
largest two terms in it.
a) What fraction of the molecules are in the ground state and what fraction in the 1st excited
state of their vibrational modes at a temperature of 700 K,
b) At what temperature will 5% of the molecules be in the 1st excited vibrational state?
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