A given molecule has 2 degenerate states that are 700 cm³¹ (wavenumbers, 1/2) above the lowest energy state. Remember that E = h * v = h * C/ where c is the speed of light. a) Calculate the temperature at which this molecule has a 15% probability to be in either of the higher energy degenerate states. b) If you were able to observe this molecule for a 100 second time period, what would be the total amount of time you observe the molecule to be in the upper degenerate energy states and what would be the total amount of time you observe the molecule to be in the lower energy state?

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Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
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It is commonly the case that 2 energy states have the same energy. States at the same
energy are known as degenerate.
A given molecule has 2 degenerate states that are 700 cm-¹ (wavenumbers, 1/2) above the
lowest energy state.
Remember that E = h * v= h * C/ where c is the speed of light.
a) Calculate the temperature at which this molecule has a 15% probability to be in either
of the higher energy degenerate states.
b) If you were able to observe this molecule for a 100 second time period, what would be
the total amount of time you observe the molecule to be in the upper degenerate energy
states and what would be the total amount of time you observe the molecule to be in the
lower energy state?
c) If there were 100 molecules present, on average about how many would be in the
upper degenerate energy states and how many would be in the lower energy state?
Transcribed Image Text:It is commonly the case that 2 energy states have the same energy. States at the same energy are known as degenerate. A given molecule has 2 degenerate states that are 700 cm-¹ (wavenumbers, 1/2) above the lowest energy state. Remember that E = h * v= h * C/ where c is the speed of light. a) Calculate the temperature at which this molecule has a 15% probability to be in either of the higher energy degenerate states. b) If you were able to observe this molecule for a 100 second time period, what would be the total amount of time you observe the molecule to be in the upper degenerate energy states and what would be the total amount of time you observe the molecule to be in the lower energy state? c) If there were 100 molecules present, on average about how many would be in the upper degenerate energy states and how many would be in the lower energy state?
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