Question

calculate the maximum wavelength of microwave radiation that will absorbed at 0k in
a)pb,Tc=7.19k
b)Al,Tc=1.2k

Answer 1

Calculate the maximum wavelength of microwave radiation that will be absorbed at 0k in a) pb, Tc=7.19k b) Al, Tc=1.2k

Solution

The Cooper pair binding energy, or gap energy, is

$$E _ {g} \approx 3 k T _ {c} \leq h \nu = \frac {h c}{\lambda}$$

From hence

$$\lambda_ {\max } = \frac {h c}{3 k T _ {c}}$$

a) $\lambda_{\max} = \frac{6.6\cdot 10^{-34}J\cdot s\cdot 3\cdot 10^{8}m / s}{3\cdot 1.38\cdot 10^{-23}\cdot J / K\cdot 7.19K} = 6.65\cdot 10^{-4}m$

b) $\lambda_{\max} = \frac{6.6\cdot 10^{-34}J\cdot s\cdot 3\cdot 10^{8}m / s}{3\cdot 1.38\cdot 10^{-23}\cdot J / K\cdot 1.2K} = 3.98\cdot 10^{-3}m$

Answer

a) $\lambda_{\max} = 6.65\cdot 10^{-4}m$

b) $\lambda_{\max} = 3.98\cdot 10^{-3}m$