Boltzmann Statistics A molecule has three degenerate excited vibrational states, each with excitation energy above the...

Boltzmann Statistics

A molecule has three degenerate excited vibrational states, each with excitation energy above the ground state

a) At temperature T, what is the ratio between the number of molecules in (all of) these excited vibrational states and the number in the ground state?

b) At very high T, what is this ratio?

c) Assume you have N distinguishable molecules of this type. Use the free energy to compute the

entropy S/k of the system at temperature T.

d) Compute the number of microstates in the equilibrium macrostate at high temperatures and

explain why your answer makes sense.

Solutions

Expert Solution

genius_generous answered 1 year ago

Next > < Previous

Related Solutions

Find the lowest two "threefold degenerate excited states" of the three-dimensional infinite square well potential for...

Find the lowest two "threefold degenerate excited states" of the three-dimensional infinite square well potential for a cubical "box." Express your answers in terms of the three quantum numbers (n1, n2, n3). Express the energy of the two excited degenerate states that you found as a multiple of the ground state (1,1,1) energy. Would these degeneracies be "broken" if the box was not cubical? Explain your answer with an example!

Show that the deuteron has no bound excited states by estimating the excited state energy and...

Show that the deuteron has no bound excited states by estimating the excited state energy and comparing it to the potential well. Consider two cases for the excited state: a) higher order radial eigenfunctions, b) non-zero angular momentum. c) If the nuclear force had a longer range R >R0 we could possibly have excited states. What would be the minimum and maximum values of R∗ so that there could be an excited state with l = 1 but no excited...

Rotational spectroscopy observe what type of molecule? What is his energy range? Measured molecule properties. vibrational...

Rotational spectroscopy observe what type of molecule? What is his energy range? Measured molecule properties. vibrational spectroscopy observe what type of molecule? What is his energy range? Measured molecule properties.

The three lowest non-degenerate energy levels of a certain molecule areE1 =0,E2 =?>0,andE3 =10?. (a)Showthatatsufficientlylow temperatures...

The three lowest non-degenerate energy levels of a certain molecule areE1 =0,E2 =?>0,andE3 =10?. (a)Showthatatsufficientlylow temperatures (how low?) only levels E1 and E2 are populated. Estimate this temperature kTc in terms of the number N of molecules and ?. Use Boltzmann statistics. (b) At any temperature T, what is the average energy of a molecule?

Discuss Vibrational Spectroscopy of a diatomic molecule (harmonic oscillator). Give the selection rule and mathematical energy...

Discuss Vibrational Spectroscopy of a diatomic molecule (harmonic oscillator). Give the selection rule and mathematical energy expressions.

Discuss Vibrational Spectroscopy of a diatomic molecule (harmonic oscillator). Give the selection rule and mathematical energy...

Discuss Vibrational Spectroscopy of a diatomic molecule (harmonic oscillator). Give the selection rule and mathematical energy expressions.

Consider a system of distinguishable particles having only three non-degenerate energy levels separated by an energy...

Consider a system of distinguishable particles having only three non-degenerate energy levels separated by an energy that is equal to the value kT at 25.0K. Calculate: 1) the ratio of populations in the states at a. 1.00K 2) the molecular partition function at 25.0K 3) the molar energy at 25.0K 4) the molar heat capacity at 25.0K 5) the molar entropy at 25.0K

we have the following statistics. maxwell-boltzmann, fermi-dirac and bose-einstein. when then sonsidering different systems which above...

we have the following statistics. maxwell-boltzmann, fermi-dirac and bose-einstein. when then sonsidering different systems which above statistics would fit the best, give a short answer of why. a) He4 under normal room conditions of temperature and pressure b) electrons in copper under normal room conditions c) He4 at lambda point d) electrons and holes in a semiconductor Ge in room temperature, band gap 1V

1) Derive the Fermi Dirac statistical distribution law. 2) Compare the three statistics Maxwell-Boltzmann statistics,Bose-Einstein statistics,Fermi-Dirac...

1) Derive the Fermi Dirac statistical distribution law. 2) Compare the three statistics Maxwell-Boltzmann statistics,Bose-Einstein statistics,Fermi-Dirac Statistics.

Sketch potential energy curves for the ground and excited states showing events leading to phosphoresce. Use...

Sketch potential energy curves for the ground and excited states showing events leading to phosphoresce. Use arrows to label all necessary transitions and answer the following: A) Based on your picture does phosphoresce occur at lower or higher wavelength relative to the absorption wavelength? B) Would you expect 0-0 transition for absorption and phosphorescence to be coincident?

Subjects