The number desnity of donor atoms which have to be added to an intrinsic germanium semiconductor to produce an n-type semiconductor of conductivity `5 ohm^(-1) cm^(-1)` is `axx10^(15)cm^(-3)`. Given that the mobility of electron in n-type Ge is `3900 cm^(2)//Vs`, Neglect the contribution of holes to conductivity. What is the integer value of a?

Explanation

Here, `sigma=5Omega^(-1)cm^(-1), mu_(e)=3900 cm^(2)//Vs, n_(e)=?`
We know that, `sigma=1/rho=e n_(e) mu_(e)`
or `n_(e)=sigma/(emu_(e))=5/((1.6xx10^(-19))xx3900)~=8xx10^(15) cm^(-3)`.
Since, one donor atom provides one free electron to the germanium semiconductor, therefore, number bensity of donor atoms `=8xx10^(15) cm^(-3)`