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Copper has one conduction electron per atom.Its density is 8.89 g/cc 4 its atomic mass is 63.54g/mol. If a Cu wire of diameter of 1nm carries a current of 2 A, what is the drift speed of electron in wire ?

Copper has one conduction electron per atom.Its density is 8.89 g/cc 4 its atomic mass is 63.54g/mol. If a Cu wire of diameter of 1nm carries a current of 2 A, what is the drift speed of electron in wire ?

Grade:Upto college level

1 Answers

AJIT AskiitiansExpert-IITD
68 Points
10 years ago

Dear Mainak ,

You Can use simple equation :

         I = neAvd   where n = no of conduction electrons /volume

                                       e = 1.6 x 10-19 c

                                       A = Area of Cross section of the wire

                                       vd = Drift velocity

calculation of n

  let us consider a seciton of length  1 m  , volume of that section  =  ∏ r2 l    = 7.85 *10-19  m3

         Mass of piece = ∏ r2 l * density  =  6.98  *10-12  g

    therefore no of moles in that amount  =  6.98  *10-12  g / 63.54 g  = 1.098 *10-13 

  no of atoms of copper in this amount  =  1.098 *10-13 * 6.022 *1023  = 6.617 * 1010  atoms  =  6.617 * 1010 electrons

there fore  , n  = 6.617 * 1010 electrons / 7.85 *10-19  m3 =  8.43  * 1028

 

now apply equations ,        2 = 8.43  * 1028 *1.6 *10-19 * 7.85 *10-19 *vd

                                            vd = 1.88 * 108  m/s 

the value comes out to be too high because the wire is of nano scale, it is still impossible to buildsuch wires.

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