If the current flowing through a copper wire of 1mm diameter is 1.1A. The density of copper is `9 g cm^(-3)` and atomic mass of copper is 63 u. One free electron is contributed by each atom of copper. Find the drift velocity of electron. Avogardo's number `=6.0 xx10^(26) ` per kg atom.

Explanation

Here, `2 r =1 mm =10^(-3)m`
or `r =1/2 xx 10^(-3) m, I=1.1A`
`d=9 g cm^(-3) =9xx10^(3) kg//m^(3)`.
Therefore, mass of `1 m^(3)` of copper ` =9 xx10^(3) kg`
Atomic mass, `M=63 u = 63kg`
Avogadro's number,
`N=6.0 xx 10^(26)` per kg atom.
So `6.0xx10^(26)` atoms of copper has a mass = 63 kg
No. of atoms per `m^(3)` of copper `=N/M//d =Nd/M`
As 1 atom contributes one conduction electron, therefore, number of conduction electrons per `m^(3)` of copper is
`n= (Nd)/(M)=((6.0xx10^(26))xx(9xx10^(23)))/(63)`
`=8.57 xx10^(28) m^(-3)`
`v_(d) =(I)/("neA")`
`=(1.1)/((8.57xx10^(28))xx(1.6 xx10^(-19))xx[(22)/(7)xx((1)/(2)xx10^(-3))^(2)])`
`~~10^(-4) m//s`