The bond force constant for the Cul (copper iodide) is 174 Nm ¹. (a) Calculate the approximate wavelength of the light absorbed due to the transition v=0→2 in Cul. (b) Estimate the isotopic shift (fractional change in wavelength) for the same transition between Cul and Cul. (c) The fraction of molecules with vibration energy level j at temperature T is given by pie (1-e) where y=hw/kBT. Calculate the temperature of a gas in which 1/2 the Cul molecules are in the vibrational ground state. (d) In general, diatomic molecules such as HCl and CO are mostly in the vibrational ground state at room temperature. Give two reasons why this is not the case for Cul.

Experimentally it appears that many polyatomic molecules' vibrational degrees of freedom can contribute to some extent to their energy at room temperature. Would you expect that fact to increase or decrease their heat capacity from the value R? Explain.

A tightly wound solenoid at 4.0 K is 50 cm long and is constructed from Nb wire of radius 1.5 mm. What maximum current can the solenoid carry if the wire is to remain superconducting?

To obtain a more clearly defined picture of the FermiDirac distribution, consider a system of 20 FermiDirac particles sharing 94 units of energy. By drawing diagrams like Figure P10.11, show that there are nine different microstates. Using Equation 10.2, calculate and plot the average number of particles in each energy level from 0 to 14E. Locate the Fermi energy at 0 K on your plot from the fact that electrons at 0 K fill all the levels consecutively up to the Fermi energy. (At 0 K the system no longer has 94 units of energy, but has the minimum amount of 90E.) 1 Microstate8 others? One of the nine equally probable microstates for 20 FD particles with a total energy of 94E.

Using the method of the preceding problem, estimate the fraction of nitric oxide (NO) molecules at a temperature of 250 K that have energies between 3.451021 J and 3.501021 J. `

As an alternative to Equation 42.1, another useful model for the potential energy of a diatomic molecule is the Morse potential U(r)=B[ea(rr0)1]2 where B, a, and r0 are parameters used to adjust the shape of the potential and its depth. (a) What is the equilibrium separation of the nuclei? (b) What is the depth of the potential well, defined as the difference in energy between the potentials minimum value and its asymptote as r approaches infinity? (c) If is the reduced mass of the system of two nuclei and assuming the potential is nearly parabolic about the well minimum, what is the vibrational frequency of the diatomic molecule in its ground state? (d) What amount of energy needs to be supplied to the ground-state molecule to separate the two nuclei to infinity?

The characteristic energy for KCl is 1.4105eV . (a) Determine for the KC1 molecule, (b) Find the separation distance between the K arid Cl atoms.

To give a helium atom nonzero angular momentum requires about 21.2 eV of energy (that is, 21.2 eV is the difference between the energies of the lowest-energy or ground state and the lowest-energy state with angular momentum). The electron-volt or eV is defined as 1.601019 J. Find the temperature T where this amount of energy equals kTB/2 . Does this explain why we can ignore the rotational energy of helium for most purposes? (The results for other monatomic gases, and for diatomic gases rotating around the axis connecting the two atoms, have comparable orders of magnitude.)

Check Your Understanding A molecule is vibrating at a frequency of 5.010Hz. What is the smallest spacing between its vibrational energy levels?

The measured density of a NaF crystal is 2.558 g/cm3 . What is the equilibrium separate distance of Na+ and Flions?