Chapter 9- Molecular Physics

[From exercise 3: Electron affinity is a property specifying the "appetite" of an element for gaining electrons. Elements, such as fluorine and oxygen, that lack only one or two electrons to complete shells can achieve a lower energy state by absorbing an extra electron. For instance, in uniting an electron with a neutral chlorine atom, completing its n=3 shell and forming a Cl^- ion, 3.61 eV of energy is liberated.]

4. Exercise 3 outlines how energy may be gotten out by transferring an electron from an atom that easily loses an electron to one with a large appetite for electrons, then allowing the two to approach, forming an ionic bond. (a) Consider separately the cases of hydrogen bonding with fluorine and sodium bonding with fluorine. In each case, how close must the ions approach to reach "break even," where the energy needed to transfer the electron between the separated atoms is balanced by the electrostatic potential energy of attraction? (The ionization energy of hydrogen is 13.6 eV, while that of sodium is 5.1 eV, and the electron affinity of fluorine is 3.40 eV.) (b) Of HF and NaF, one is considered to be an ionic bond anf the other is a covalent bond. Which is which, and why?

10. The bond length of the N₂ molecule is 0.11 nm and its effective spring constant is 2.3x10³ N/m. (a) From the size of the energy jumps for roataion and vibration, determine whether either of these modes of energy storage should be active at 300 K. (b) According the the equipartition theorem, the heat capacity of a diatomic molecule storing energy in rotations but not vibrations should be 5/2 R (3 translational + 2 rotational degrees of freedom), while if also storing energy in vibrations, it should be 7/2 R (adding 2 vibrational degrees). Nitrogen's molar heat capacity is 20.8 J/mole-K at 300 K. Does this agree with your findings in part (a)?

11. The effective force constant of the molecular "spring" in HCl is 480 N/m and the bond length is 0.13 nm. (a) Determine the energies of the two lowest-energy vibrational states. (b) For these energies, determine the amplitude of vibration if the atoms could be treated as oscillating classical particles. (c) For these energies, by what percent does the atomic separation fluctuate? (d) Calculate the classical vibration frequency w_vib = [k/m]^1/2 and rotational frequency w_rot = L/I. For the rotational frequency, assume that L is its lowest nonzero value, [1(1+1)]^1/2h/2p, and that the moment of inertia I is ma². (e) Is it valid to treat the atomic separation as fixed for rotational motion while changing for vibrational?

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