What is the temperature of a two-level system of energy separation equivalent to 400 cm−1 when the population of the upper state is one-third that of the lower state?
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What is the temperature of a two-level system of energy separation equivalent to 400 cm−1 when the population of the upper state is one-third that of the lower state?
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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?Suppose two different states (with no degeneracy so that g1=g2=1) have energies E2=2x10-22 J and E1=0.5x10-22 J. At what temperature will N2 have a population so that the rato of N2/N1=100? Suppose now that the degeneracies are g1=3, g2=2. Is it possible to find a temperature where the population in N2 is larger than N1?Chemistry The first excited electronic energy level of the helium atom is 3.13 ✕ 10−18 J above the ground level. Estimate the temperature at which the electronic motion will begin to make a significant contribution to the heat capacity. That is, at what temperature will 5.0% of the population be in the first excited state?
- We discussed in class (several times) how the Boltzmann distribution can be used to relate the relative populations of two states differing in energy by AU. Suppose you are given a vial containing a solution of glucose in water (don't ask why this would happen). For the purpose of this question, glucose exists in one of two conformations-"chair" or "boat"-with an energy difference (AU) of 25.11 kJ mol1 between them. 1. What would be the proportion of molecules in the "boat" conformation at 310K? 2. Thinking back to our discussion of the individual sources of energy that go into the potential energy calculation for a molecule (e.g. Upond Uangle, Uelectrostatic. etc), give a plausible explanation of why the "boat" conformation is less stable. H он "Chair" OH "Вoat" но но но- HO. H. HO. HO H. HO. OHCalculate the vibrational, rotational, and translational contributions to the constant volume heat capacity (Cv) for 14N2 at 298 K. Assume this represents the high temperature limit for rotational energy and low temperature limit for vibrational energy. Given that Cv=20.81 J/K·mol for N2, state which type or types of energy contribute most to Cv for N2 and explain why those types of energy contribute most.Discuss the relation between the thermodynamic and statistical definitions of entropy.
- Calculate the molar internal energy of a monatomic gas.The cohesive energy density, U, is defined as U/V, where U is the mean potential energy of attraction within the sample and V its volume. Show that U = 1/2N2∫V(R)dτ where N is the number density of the molecules and V(R) is their attractive potential energy and where the integration ranges from d to infinity and over all angles. Go on to show that the cohesive energy density of a uniform distribution of molecules that interact by a van der Waals attraction of the form −C6/R6 is equal to −(2π/3)(NA2/d3M2)ρ2C6, where ρ is the mass density of the solid sample and M is the molar mass of the molecules.The heat capacity ratio of a gas determines the speed of sound in it through the formula cs = (γRT/M)1/2, where γ = Cp,m/CV,m and M is the molar mass of the gas. Deduce an expression for the speed of sound in a perfect gas of (a) diatomic, (b) linear triatomic, (c) nonlinear triatomic molecules at high temperatures (with translation and rotation active). Estimate the speed of sound in air at 25 °C. Hint: Note that Cp,m − CV,m = R for a perfect gas.
- The internal energy of a system A None of these В is the sum of the rotational, vibrational, and translational energies of all of its components refers only to the energies of the nuclei of the atoms of the component molecules D is the sum of the kinetic energy of all of its components E) is the sum of the potential and kinetic energies of the componentsWhy is it important to distinguish between the standardstate and the reference state of an element?Use the equipartition theorem to estimate the constant-volume molar heat capacity of (i) I2, (ii) CH4, (iii) C6H6 in the gas phase at 25 °C.