(a) For the hypothetical system listed below, calculate the partition function at 500 K. (b) What...
5) Calculate the total molecular partition function for 2 moles of Oz gas at 292.5 K and 24 atm. You can assume ideal behavior (V=nRT/P). For O2 the rotational constant is B = 1.45 cm and the vibrational frequency is 1580 cm. The ground state electronic level has a degeneracy of 3.
Problem 4. Calculate the vibrational partition function of CS, at 500 K given the wavelength 558 cm (symmetric stretch), 397 cm (bend; two modes), and 2097 cm (asymmetric stretch)
For a spin-1/2 particle in a magnetic field B, with energies and , (a) calculate the partition function. (b) Show that the mean energy of this particle is given by ̅ For a system of noninteracting spins, (c) what is the total partition function and (d) mean energy? We were unable to transcribe this image2 2kT 2 2kT
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4.) Calculate the rotational partition function for Hy at 1000 K, where B=60.589 cm 1
2. Consider a closed system with three possible energy values, 0, E, and 2€, under constant V and T condition. The third energy level with E = 2€, however, has a degeneracy of y: i.e. There are y states that have the identical energy value of 2€. (a) Express the partition function in terms of 7 €, and T. (b) Write the probability to sample each energy level (P1, P2, and P3) in terms of 7, €, and T. (c)...
Question 9 Consider a quantum system comprising two indistinguishable particles which can occupy only three individual-particle energy levels, with energies 81 0, 82 2 and E3 38.The system is in thermal equilibrium at temperature T. (a) Suppose the particles which can occupy an energy level. are spinless, and there is no limit to the number of particles (i) How many states do you expect this system to have? Justify your answer (ii) Make a table showing, for each state of...
-2 points Calculate the translational partition function at (a) 300 K and (b) 600 K of a molecule of molar mass 280 g mol'" in a container of volume 2.30 cm2. Ger at 300 K Qu at 600 K Note: this i s a measure of the vast number of accessible microstates of translation available to a molecule under these conditions.
1. Calculate (a) the thermal wave-length (in pm) and (b) the translational partition function of H atom in a cubic box of side 1.0 cm at 300 K. (c) Can a hydrogern molecule be considered as a classical system (as a diatomic molecule in whiclh hydrogen atoms behave classically) at this temperature? Explain why.
Vibration energy levels are evenly spaced. Calculate the vibrational partition function at 500.0 K for a diatomic molecule whose εvibrational is 1.19e-20 J. What fraction of the molecules would have vibrational energy 1ε=1.19e-20 J?
2. Consider a closed system with three possible energy values, O, E, and 2€, under constant V and T condition. The third energy level with E = 2€, however, has a degeneracy of y: i.e. There are states that have the identical energy value of 2€. (a) Express the partition function in terms of %, E, and T. (b) Write the probability to sample each energy level (P1, P2, and P3) in terms of 7, €, and T. (c) Write...