9.8 Superconductivity

Resistance vanishing below a critical temperature, magnetic flux expulsion, Cooper pairing in BCS theory, and critical fields and currents from measured data.

University Physics Volume 3, 9.8 Superconductivity

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15 exercises

9.8 Exercise 1

What conditions are necessary for superconductivity?

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9.8 Exercise 3

How does BCS theory explain superconductivity?

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9.8 Exercise 5

What impact does an increasing magnetic field have on the critical temperature of a semiconductor?

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9.8 Exercise 6

At what temperature, in terms of $T_{C}$ , is the critical field of a superconductor one-half its value at $T = 0 \text{K}$ ?

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9.8 Exercise 8

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 $50 - \Omega$ 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?

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9.8 Exercise 10

Potassium fluoride (KF) is a molecule formed by an ionic bond. At equilibrium separation the atoms are $r_{0} = 0.255 \text{nm}$ 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.)

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9.8 Exercise 12

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

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9.8 Exercise 14

Determine the lowest three rotational energy levels of $\text{H}_{2} .$

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9.8 Exercise 16

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

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9.8 Exercise 18

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

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9.8 Exercise 20

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

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9.8 Exercise 22

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

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9.8 Exercise 24

Determine the Fermi energies for (a) Mg, (b) Na, and (c) Zn.

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9.8 Exercise 26

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

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9.8 Exercise 28

For an electron in a three-dimensional metal, show that the average energy is given by $\overset{−}{E} = \frac{1}{N} \int_{0}^{E_{\text{F}}} E g \left(E\right) d E = \frac{3}{5} E_{\text{F}} ,$

Where N is the total number electrons in the metal.

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