An intrinsic semiconductor has a resistivity of 0.50 `Omega` m at room temperature. Find the intrinsic carrier concentration if the mobilities of electrons and holes are `0.39 m^2 V^(-1) s^(-1)` and `0.11 m^2 V^(-1) s^(-1)` respectively

Options

A. `1.2xx10^(18)//m^(3)`
B. `2.5xx10^(19)//m^(3)`
C. `1.9xx10^(20)//m^(3)`
D. `3.1xx10^(21)//m^(3)`

Answer

B

Explanation

Here, `rho=0.50Omegam`
`mu_(e)=0.39m^(2)//Vs, mu_(h)=0.11m^(2)//Vs`
The resistivity of intrinsic semiconductor is `(1)/(rho)=e(n_(i)mu_(e)+n_(i)mu_(h))`
Where `n_(i)=(1)/(rhoe(mu_(e)+mu_(h)))`
Substituting the given values, we get
`n_(i)=(1)/(((0.5)(1.6xx10^(-19)))(0.39+0.11))=2.5xx10^(19)//m^(3)`