Copper has one conduction electron per atom. Its density is `8.89 g//cm^3` and its atomic mass. `63.54 g//mol`. If a copper wire of diameter `1.0 mm` carries a current of `2.0 A`, what is the drift speed of the electrons in the wire?

Answer

A, D

Explanation

`rho=8.89xx10^3kg/m^3`
Mass of `1m^3=8.89xx10^3=8.89xx10^6g`
`:.` Number of gram moles `=(8.89xx10^6)/63.54=1.4x10^5`
Number of atoms `=1.4xx10^5xx6.02xx10^23`
`=8.42xx10^28`
One atom emits one condition electron.
therefore number of free electrons in unit volume (or `1m^3` volume)
`n=8.42xx10^28per m^3`
`No2, i="ne"Av_d`
`:. v_d=1/("ne"A)=i/("ne"pi r^2)`
`=2.0/((8.42xx10^28)(1.6xx10^-19)(pi)(0.5xx10^-3)^2)`
`=1.9xx10^-4m//s`