A current of `4.4A` is flowing in a copper wire of radius `1mm` density of copper is `9 xx 10^(3)kg m^(-3)`and its atoms is `63.5u` If every atoms of copper contributes one condition electron , then the drift velocity of electrons is nearly [density of copper `9 xx 10^(3) kg m^(3)]`

Options

A. `0.1mm s^(-1)`
B. `0.5mm s^(-1)`
C. `1mm s^(-1)`
D. `1.5mm s^(-1)`

Answer

A

Explanation

Atomic mass of copper `M = 63.5g = 0.0635 kg`
No of copper atoms in `0.0635kg` coppere `= 6.02 xx 10^(23)`
Density of copper `= (M)/(d) = (0.0635)/(9 xx 10^(3)) m^(3)`
Total no of atoms in unit volume of copper
`= (9 xx 10^(3))/(0.0635) xx 6.02 xx 10^(23) = 8.5 xx 10^(28) "atoms"//m^(-3)`
As one atom of copper contributes one conduction electron to so the electron density of copper
`n = 8.5 xx 10^(28)m^(-3)`
Drift velocity`v_(d) = (1)/(n Ae)`
`= (44)/((6.5 xx 10^(28)) xx pi(0.001)^(2) xx (1.6 xx 10^(-19))`
`0.1 xx 10^(-3)m//s = 0.1mm//s`