Question

Copper has one conduction electron per atom. Its density is $8.89g/m^3$ and its atomic mass is 63.54 g/mol. lf 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?

• A. $1.9\times {10}^{-4}$
• B. $2.9\times {10}^{-4}$
• C. $1.9\times {10}^4$
• D. $2.9\times {10}^4$

Answer 1

The correct option is A $1.9\times {10}^{-4}$

Given : $\rho =8.89$ $g/c{m}^3=8.89\times {10}^6$ $g/m^3$

$M=63.54$ $g/mol$ $d={10}^{-3}m$ $I=2$ A

Copper atoms per unit volume $n_{cu}=\frac{\rho N_A}{M}=\frac{8.89\times {10}^6\times 6.023\times {10}^{23}}{63.54}=8.43\times {10}^{28}$ Cu atoms per $m^3$

As one Cu atom gives one conduction electron.

$⟹$ Number of conduction electrons $n_e=8.43\times {10}^{28}$ electrons per $m^3$

Cross-sectional area of wire $A=\frac{\pi d^2}{4}=\frac{\pi ({10}^{-3}{)}^2}{4}=7.85\times {10}^{-7}$ $m^2$

$\therefore$ Drift velocity $V_d=\frac{I}{Aq{n}_e}=\frac{2}{(7.85\times {10}^{-7})(1.6\times {10}^{-19})(8.43\times {10}^{28})}=1.9\times {10}^{-4}$ m/s