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For one mole of argon gas at 450 K and 1 atm, calculate the qtotal. The ground electronic state has a degeneracy of 4.
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- The force constant for HBr is 412 N m-1. Using the harmonic oscillator model, calculate the relative population of the first excited state and the ground state at 300 K.The force constant for HF is 966 N m-1. Using the harmonic oscillator model, calculate the relative population of the first excited state and the ground state at 300 K.Derive an expression for the mean energy of a collection of molecules that have three energy levels at 0, ε, and 3ε with degeneracies 1, 5, and 3, respectively.
- 1.3 The ground level of Cl is 2P3/2 and a 2P1/2 level lies 881 cm-1 there above. Calculate the electronic contribution to the heat capacity of Cl atoms at 500 K.1. The energy gap between the ground state and next levels in NO is A=15.4 meV. Find the electronic contribution to the molar heat capacity at T₁ = 50 K and T₂= 500 K.Differentiate between Fermi level and Fermion.
- The three normal modes of water are the symmetric stretch (3652 cm¹), the antisymmetric stretch (3756 cm¹), and the bend (1595 cm¹). (a) Calculate the molecular vibrational partition function of water at 500 K. (b) At 500 K, what fraction of water molecules have the bend excited to v₂=1. What fraction of water molecules have the symmetric stretch excited to v₁=1? Why do more molecules have the bend excited? (c) At 500 K, what fraction of water molecules have both v2-1 and v₁=1 excited?(c) Consider the following rotational temperatures of diatomic molecules: qr(N2) = 2.9K, qr(HD) = 64.7K Assuming classical behaviour (i.e. continuum approximation): (i) Estimate the number of accessible rotational energy levels at 290 K for both molecules14.44) The lowest triplet state in naphthalene (C10H8) is about 11,000 cm-1 below then lowest excited singlet electronic level at 77 K. Calculate the ratio of the population in these two states. [Hint: The Boltzmann equation is given by N2/N1 = (g2/g1 exp(-ΔE/kBT), where g1 and g2 are the degeneracies for level 1 and 2.]
- Identify the systems for which it is essential to include a factor of 1/N! on going from Q to q : (i) a sample of helium gas, (ii) a sample of carbon monoxide gas, (iii) a solid sample of carbon monoxide, (iv) water vapour.A certain atom has a doubly degenerate ground level , a triply degenerate electronically excited level at 12050 cm-1, and doubly degenerate level at 1300 cm-1. Calculate the electronic contribution to the molar internal energy at 2000 K for a sample composed of the atoms1. A certain atom has a nondegenerate ground level, a triply degenerate level at 1025 cm-1 and a doubly degenerate level at 1100 cm-1. Calculate the electronic contribution to the molar internal energy at 1500K for a sample composed of these atoms.