Estimate the energy gap Eg for niobium at T = 0, and find the minimum photon wavelength needed to break the Cooper pair. Strategy From Table 10.5 we see that Tc = 9.25 K for Nb. Therefore Equation (10.46) can be used to compute the energy gap. The photon wavelength can then be found using the usual

Question

Estimate the energy gap [latex]E_{ g }[/latex] for niobium at T = 0, and find the minimum photon wavelength needed to break the Cooper pair.

Strategy From Table 10.5 we see that [latex]T_{ c }=9.25[/latex] K for Nb. Therefore Equation (10.46) can be used to compute the energy gap. The photon wavelength can then be found using the usual formula relating energy and wavelength, [latex]E=h c / \lambda[/latex].

[latex]E_{ g }(0) \approx 3.54 k T_{ c }[/latex] (10.46)

Accepted Answer

From Equation (10.46),

[latex]\begin{aligned}E_{ g } \approx 3.54\left(1.38 imes 10^{-23} J / K ight)(9.25 K ) &=4.52 imes 10^{-22} J \&=2.82 meV\end{aligned}[/latex]

This small energy corresponds to a photon wavelength of

[latex]\lambda=h c / E_{ g }=4.39 imes 10^{-4} m[/latex]

This is in the far-infrared region of the electromagnetic spectrum. Photons with this wavelength or lower have sufficient energy to break the Cooper pair in niobium. Note that this estimate of [latex]E_{g}[/latex] is close to the experimental value of 3.03 meV.

Question 10.7: Estimate the energy gap Eg for niobium at T = 0, and find th...

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