# Thermodynamics

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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 -

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 -

Perfect. I do remember reading that before. Thanks so much for the help!

• Thermodynamics -

i like feet

• Thermodynamics -

436

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