At very low temperatures the photoelectric threshold short wavelength in an impurity-free germanium is equal to `lambda_(th)= 1.7 mu m`. Find the temperature coefficient of resistance of this germanium sample at room temperature.

Explanation

The Photelectric threshold determines the band gap `Delta epsilon` by
`Delta epsilon=(2pi ħc)/(lambda_(th))`
On the other hand the temperature coefficient of resistance is defined by(`rho` is respectively)
`alpha=(1)/(rho) (d rho)/(dT)=(d)/(dT) In rho=(d)/(dT) In sigma`
where `sigma` is the conductivity. But
In `sigma= In sigma_(0)-(Delta epsilon)/(2KT)`
Then `alpha=(Delta epsilon)/(2kT^(2))= -(pi ħ c)/(kT^(2) lambda_(th))= -0.047K^(-1)`