### Additional Problems

Potassium fluoride (KF) is a molecule formed by an ionic bond. At equilibrium separation the atoms are ${r}_{0}=0.255\phantom{\rule{0.2em}{0ex}}\text{nm}$ apart. Determine the electrostatic potential energy of the atoms. The electron affinity of F is 3.40 eV and the ionization energy of K is 4.34 eV. Determine dissociation energy. (Neglect the energy of repulsion.)

For the preceding problem, sketch the potential energy versus separation graph for the bonding of ${\text{K}}^{+}\phantom{\rule{0.2em}{0ex}}\text{and}\phantom{\rule{0.2em}{0ex}}{\text{Fl}}^{\text{\u2212}}$ ions. (a) Label the graph with the energy required to transfer an electron from K ^{}to Fl. (b) Label the graph with the dissociation energy.

The separation between hydrogen atoms in a ${\text{H}}_{2}$ molecule is about 0.075 nm. Determine the characteristic energy of rotation in eV.

The characteristic energy of the ${\text{Cl}}_{2}$ molecule is $2.95\phantom{\rule{0.2em}{0ex}}\times \phantom{\rule{0.2em}{0ex}}{10}^{\mathrm{-5}}\phantom{\rule{0.2em}{0ex}}\text{eV}$. Determine the separation distance between the nitrogen atoms.

A carbon atom can hybridize in the $s{p}^{2}$ configuration. (a) What is the angle between the hybrid orbitals?

List five main characteristics of ionic crystals that result from their high dissociation energy.

Why is bonding in ${\text{H}}_{2}{}^{+}$ favorable? Express your answer in terms of the symmetry of the electron wave function.

Astronomers claim to find evidence of ${\text{He}}_{2}$ from light spectra of a distant star. Do you believe them?

Show that the moment of inertia of a diatomic molecule is $I=\mu {r}_{0}^{2}$, where $\mu $ is the reduced mass, and ${r}_{0}$ is the distance between the masses.

Show that the average energy of an electron in a one-dimensional metal is related to the Fermi energy by $\stackrel{\text{\u2212}}{E}=\frac{1}{2}{E}_{\text{F}}.$

Measurements of a superconductor’s critical magnetic field (in *T*) at various temperatures (in K) are given below. Use a line of best fit to determine ${B}_{\text{c}}(0).$ Assume ${T}_{\text{c}}=9.3\phantom{\rule{0.2em}{0ex}}\text{K}\text{.}$

T (in K) | ${B}_{\text{c}}(T)$ |
---|---|

3.0 | 0.18 |

4.0 | 0.16 |

5.0 | 0.14 |

6.0 | 0.12 |

7.0 | 0.09 |

8.0 | 0.05 |

9.0 | 0.01 |

Estimate the fraction of Si atoms that must be replaced by As atoms in order to form an impurity band.

Transition in the rotation spectrum are observed at ordinary room temperature ($T=300\phantom{\rule{0.2em}{0ex}}\text{K}$). According to your lab partner, a peak in the spectrum corresponds to a transition from the $l=4$ to the $l=1$ state. Is this possible? If so, determine the momentum of inertia of the molecule.

Find the average energy of an electron in a Zn wire.

What value of the repulsion constant, *n*, gives the measured dissociation energy of 158 kcal/mol for CsCl?

A physical model of a diamond suggests a BCC packing structure. Why is this not possible?