The density of an electron - hole pair in a pure germanium is `3xx10^(-16) m^(-3)` at room temperature. On doping with aluminium , the hole density increase to `4.5xx10^(22) m^(-3)` Now the electron density ( in m ) in doped germanium will be

Options

A. `1xx10^(10)`
B. `2 xx10^(10)`
C. `0.5 xx10^(10)`
D. `4 xx10^(10)`

Answer

B

Explanation

In pure germanium , `n_i=n_e=n_n=3xx10^(16)m^(-3)`
In doped germanium , `n_i^2=n_en_h`
`:.n_e=(n_i^2)/n_h=((3xx10^(16)m^(-3))^2)/(4.5xx10^(22)m^(-3))=(9xx10^(32))/(4.5xx10^(22))m^(-3)`
`=2xx10^(10)m^(3)`
Thus, the electron density in doped germanium will be `2xx10^(10) m^(-3)`