Posted by **chemstudent** on Monday, February 23, 2009 at 2:51am.

What is the temperature of a two-level system of energy separation equivalent to 300 cm^−1 when the population of the upper state is one-half that of the lower state?

What does this "energy separation equivalent to 300 cm^−1" mean?

I can get this far:

n1 = 1/2 n0 = 1/2

e^(-E/kT) = 1/2

e^(E/kT) = 2

E/kT = ln 2

T = E / (k * ln 2)

But here, I am stuck. I don't know how to get the E value from the 300 cm^-1...

- Thermodynamics -
**drwls**, Monday, February 23, 2009 at 2:58am
To get energy E from wavenumber w, use the equation

E = h c w

c is the speed of light and h is Planck's constant. The equation is equivalent to E = h * frequency

"wavenumber separation" is proportional to "energy separation" between two quantum states. They call is "wavenumbers" because it is the number of waves per unit distance along the emitted light beam. It equals one divided by the wavelength.

- Thermodynamics -
**chemstudent**, Monday, February 23, 2009 at 10:21am
Perfect. I do remember reading that before. Thanks so much for the help!

- Thermodynamics -
**wong**, Wednesday, March 6, 2013 at 2:17pm
i like feet

- Thermodynamics -
**yimam**, Friday, August 7, 2015 at 3:37pm
436

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