The intrinsic conductivity of germanium at `27^(@)C` is `2.13ohm^(-1)*m^(-1)`, the mobilities of electrons and holes are 0.38 and `0.18m^(2)//(V*s)`, respectively. Compute the carrier densities and the Hall coefficient.

Answer

`n=2.4xx10^(19)m^(-3);R_(H)=9.4xx10^(-2)m^(3)//C`

Explanation

In the case of intrinsic conductivity, the electron and the hole concentrations are equal. Therefore `gamma=en(b_(+)+b_(-))`, where `b_(+)` is the mobility of holes and `b_(-)` is the mobility of electrons. Hence `n=(gamma)/(e(b_(+)+b_(-)))`.
To find the Hall coefficient, note that the Hall potential difference of the electron and the hole components are of opposite signs
We have
`R_(H)=R_(H)^((-))-R_(H)^((+))=(b_(-)-b_(+))/gamma`.