Question: The critical temperature lead is 7.2 K. What is the binding energy of its Cooper pairs at zero temperature?

Short Answer

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Answer

The binding energy of the Cooper pairs is 217meV.

Step by step solution

01

Given data

The critical temperature of lead is, 7.2 K .

Temperature of cooper pairs is, 0K .

02

Definition of Binding Energy

The superconducting energy gap Eg , the energy needed to split a molecule into its individual atoms, must be equivalent to the energy needed to break a cooper pair.

As per BCS theory, energy at absolute zero shall beEg=3.5kBTc .

Where KB represents Boltzmann's constant andTc represents critical temperature.

03

Determine the Binding Energy

The binding energy of the Cooper pairs is expressed as,

.Eg=3.5kBTc

Substitute 7.2KTc, and 1.38×10-23J/KkB in the above equation.

Eg=3.5kBTc=3.51.38×10-23J/K(7.2K)=3.48×10-22J1cV1.6×10-19J=2.175×10-3eV1mcV10-3eV

Which gives, Eg=2.17meV.

The binding energy of the Cooper pairs is 2.17meV.

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