Discussion
The wavelength of the photon which will be required to break a Cooper pair in a superconductor like aluminium whose critical temperature is 1.2 K is :
Answer: B
The wavelength is about 3.4 × 10-3 m.
BCS theory gives the energy gap \(2\Delta \approx 3.5\,k_{B}T_{c}\); a photon must supply this to break a Cooper pair:
\[ \begin{aligned} 2\Delta &= 3.5 \times 1.38 \times 10^{-23} \times 1.2 \approx 5.8 \times 10^{-23}\ \text{J} \\ \lambda &= \frac{hc}{2\Delta} \\ &= \frac{1.99 \times 10^{-25}}{5.8 \times 10^{-23}} \approx 3.4 \times 10^{-3}\ \text{m} \end{aligned} \]
This is in the microwave or far-infrared region. Using \(\Delta\) instead of \(2\Delta\) would double the wavelength, to about 6.8 mm, which is not offered; 2.5, 4.4 and 5.4 mm do not follow from the BCS gap.
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