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Electrostatic energy for equilibrium separation distance between atoms | ${U}_{\text{coul}}=-\frac{k{e}^{2}}{{r}_{0}}$ |
Energy change associated with ionic bonding | ${U}_{\text{form}}={E}_{\text{transfer}}+{U}_{\text{coul}}+{U}_{\text{ex}}$ |
Critical magnetic field of a superconductor | ${B}_{\text{c}}\left(T\right)={B}_{\text{c}}\left(0\right)\left[1-{\left(\frac{T}{{T}_{\text{c}}}\right)}^{2}\right]$ |
Rotational energy of a diatomic molecule | ${E}_{r}=l\left(l+1\right)\frac{{\hslash}^{2}}{2I}$ |
Characteristic rotational energy of a molecule | ${E}_{0r}=\frac{{\hslash}^{2}}{2I}$ |
Potential energy associated with the exclusion principle | ${U}_{\text{ex}}=\frac{A}{{r}^{n}}$ |
Dissociation energy of a solid | ${U}_{\text{diss}}=\alpha \frac{k{e}^{2}}{{r}_{0}}\left(1-\frac{1}{n}\right)$ |
Moment of inertia of a diatomic molecule with reduced mass $\mu $ | $I=\mu {r}_{0}^{2}$ |
Electron energy in a metal | $E=\frac{{\pi}^{2}{\hslash}^{2}}{2m{L}^{2}}\left({n}_{1}^{2}+{n}_{2}^{2}+{n}_{3}^{2}\right)$ |
Electron density of states of a metal | $g\left(E\right)=\frac{\pi V}{2}{\left(\frac{8{m}_{e}}{{h}^{2}}\right)}^{3\text{/}2}\phantom{\rule{0.2em}{0ex}}{E}^{1\text{/}2}$ |
Fermi energy | ${E}_{\text{F}}=\frac{{h}^{2}}{8{m}_{e}}{\left(\frac{3N}{\pi V}\right)}^{2\text{/}3}$ |
Fermi temperature | ${T}_{\text{F}}=\frac{{E}_{\text{F}}}{{k}_{\text{B}}}$ |
Hall effect | ${V}_{\text{H}}=uBw$ |
Current versus bias voltage across p-n junction | ${I}_{\text{net}}={I}_{0}\left({e}^{e{V}_{b}\text{/}{k}_{\text{B}}T}-1\right)$ |
Current gain | ${I}_{c}=\beta {I}_{B}$ |
Selection rule for rotational energy transitions | $\text{\Delta}l=\pm 1$ |
Selection rule for vibrational energy transitions | $\text{\Delta}n=\pm 1$ |
Describe two main features of a superconductor.
How does BCS theory explain superconductivity?
BSC theory explains superconductivity in terms of the interactions between electron pairs (Cooper pairs). One electron in a pair interacts with the lattice, which interacts with the second electron. The combine electron-lattice-electron interaction binds the electron pair together in a way that overcomes their mutual repulsion.
What is the Meissner effect?
What impact does an increasing magnetic field have on the critical temperature of a semiconductor?
As the magnitude of the magnetic field is increased, the critical temperature decreases.
At what temperature, in terms of ${T}_{C}$ , is the critical field of a superconductor one-half its value at $T=0\phantom{\rule{0.2em}{0ex}}\text{K}$ ?
$T=0.707\phantom{\rule{0.2em}{0ex}}{T}_{\text{c}}$
What is the critical magnetic field for lead at $T=2.8\phantom{\rule{0.2em}{0ex}}\text{K}$ ?
A Pb wire wound in a tight solenoid of diameter of 4.0 mm is cooled to a temperature of 5.0 K. The wire is connected in series with a $50\text{-}\text{\Omega}$ resistor and a variable source of emf. As the emf is increased, what value does it have when the superconductivity of the wire is destroyed?
61 kV
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?
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.)
$\begin{array}{ccc}\hfill {U}_{\text{coul}}& =\hfill & \mathrm{-5.65}\phantom{\rule{0.2em}{0ex}}\text{eV}\hfill \\ \hfill {E}_{\text{form}}& =\hfill & \mathrm{-4.71}\phantom{\rule{0.2em}{0ex}}\text{eV},\phantom{\rule{0.2em}{0ex}}{E}_{\text{diss}}=4.71\phantom{\rule{0.2em}{0ex}}\text{eV}\hfill \end{array}$
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.
${E}_{0r}=7.43\phantom{\rule{0.2em}{0ex}}\times \phantom{\rule{0.2em}{0ex}}{10}^{\mathrm{-3}}\phantom{\rule{0.2em}{0ex}}\text{eV}$
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.
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