Calculate the average drift speed of electrons traveling through a copper wire with a crosssectional area of 80 mm2 when carrying a current of 30 a (values similar to those for the electric wire to your study lamp). assume one electron per atom of copper contributes to the current. the atomic mass of copper is 63.5 g/mol and its density is 8.93 g/cm3 . avogadro’s number is 6.022 × 1023 and the fundamental charge is 1.602 × 10−19 c. answer in units of m/s.

The correct answer is

Explanation:

The formula for the electron drift speed is given as follows,

where n is the number of of electrons per unit m³, q is the charge on an electron and A is the cross-sectional area of the copper wire and I is the current. We see that we already have A , q and I. The only thing left to calculate is the electron density n that is the number of electrons per unit volume.

Using the information provided in the question we can see that the number of moles of copper atoms in a cm³ of volume of the conductor is . Converting this number to m³ using very elementary unit conversion we get . If we multiply this number by the Avagardo number which is the number of atoms per mol of any gas , we get the number of atoms per m³ which in this case is equal to the number of electron per m³ because one electron per atom of copper contribute to the current. So we get,

if we convert the area from mm³ to m³ we get .So now that we have n, we plug in all the values of A ,I ,q and n into the main equation to obtain,

which is our final answer.

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