A piece of pure semiconductor of silicn of size `1cm xx 1 cm xx 1 mm` is having `5 xx 10^(28)` number of atoms per cubic metre. It is doped simultaneously with `5 xx 10^(22)` atoms per `m^(3)` of aresenic adn `5 xx 10^(20)` per `m^(3)` atoms of indium. The number density of intrisic current carrier (electrons adn holes) in the pure silicon semiconductor is `1.5 xx 10^(16) m^(-3)`. Mobility of electron is `3800 cm^(2) V^(-)S^(-1)`
The number of holes in this semiconductor are

Options

A. `5.0xx10^(20)`
B. `4.54xx10^(13)`
C. `4.54xx10^(9)`
D. `4.54xx10^(2)`

Answer

D

Explanation

Number density of holes,
`n_(h)=n_(i)^(2)/n_(e)=((1.5xx10^(16))^(2))/((4.95xx10^(22)))=4.54xx10^(9)m^(-3)`
Number of holes in the given semiconductor
`=n_(e)xxvolume`
`=(4.54xx10^(9))xx(1/100xx1/100xx1/1000)`
`=4.54xx10^(2)`