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Key equations

Electrostatic energy for equilibrium separation distance between atoms U coul = k e 2 r 0
Energy change associated with ionic bonding U form = E transfer + U coul + U ex
Critical magnetic field of a superconductor B c ( T ) = B c ( 0 ) [ 1 ( T T c ) 2 ]
Rotational energy of a diatomic molecule E r = l ( l + 1 ) 2 2 I
Characteristic rotational energy of a molecule E 0 r = 2 2 I
Potential energy associated with the exclusion principle U ex = A r n
Dissociation energy of a solid U diss = α k e 2 r 0 ( 1 1 n )
Moment of inertia of a diatomic molecule with reduced mass μ I = μ r 0 2
Electron energy in a metal E = π 2 2 2 m L 2 ( n 1 2 + n 2 2 + n 3 2 )
Electron density of states of a metal g ( E ) = π V 2 ( 8 m e h 2 ) 3 / 2 E 1 / 2
Fermi energy E F = h 2 8 m e ( 3 N π V ) 2 / 3
Fermi temperature T F = E F k B
Hall effect V H = u B w
Current versus bias voltage across p-n junction I net = I 0 ( e e V b / k B T 1 )
Current gain I c = β I B
Selection rule for rotational energy transitions Δ l = ± 1
Selection rule for vibrational energy transitions Δ n = ± 1

Conceptual questions

Describe two main features of a superconductor.

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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.

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What is the Meissner effect?

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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.

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Problems

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

T = 0.707 T c

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What is the critical magnetic field for lead at T = 2.8 K ?

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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 - Ω 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

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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?

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Additional problems

Potassium fluoride (KF) is a molecule formed by an ionic bond. At equilibrium separation the atoms are r 0 = 0.255 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.)

U coul = −5.65 eV E form = −4.71 eV , E diss = 4.71 eV

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For the preceding problem, sketch the potential energy versus separation graph for the bonding of K + and Fl 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.

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The separation between hydrogen atoms in a H 2 molecule is about 0.075 nm. Determine the characteristic energy of rotation in eV.

E 0 r = 7.43 × 10 −3 eV

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The characteristic energy of the Cl 2 molecule is 2.95 × 10 −5 eV . Determine the separation distance between the nitrogen atoms.

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Practice Key Terms 6

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Source:  OpenStax, University physics volume 3. OpenStax CNX. Nov 04, 2016 Download for free at http://cnx.org/content/col12067/1.4
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