amount of charge of electrons present in 10gram of aluminium rod?
Answers
An aluminum wire with a cross-sectional area of 4 x 10- 6 m 2 carries a current of 5 A. Find the drift speed of the electrons in the wire, assuming each aluminum atom contributes on electron. The density of aluminum is 2.7 g/cm 3.
Solution:
For this we will use
I = nqvdA.
To find the number of charges per unit volume, n , we find from the periodic table that the atomic mass of aluminum is 26.98 g/mol. Since 1 mol of a substance contains Avagadro's number NA = 6.02 x 1023 of particles, we find
n = 6.02 x 1023$\displaystyle{\frac{{\:\rm electrons}}{{\:\rm mole}}}$ x $\displaystyle{\frac{1\ {\:\rm mole}}{26.98\ {\:\rm g}}}$ x $\displaystyle{\frac{2.7\ {\:\rm g}}{1\ {\:\rm cm}{}^3}}$ x $\displaystyle\left(\frac{100\ {\:\rm cm}}{1\ {\:\rm m}}\right)$3 = 6.02 x 1028$\displaystyle{\frac{{\:\rm electrons}}{{\:\rm m}{}^3}}$
We then find
vd = $\displaystyle{\frac{I}{nqA}}$ = $\displaystyle{\textstyle\frac{5}{6.02\times 10^{28}\cdot
1.6\times 10^{-19}\cdot 4\times 10^{-6}}}$ = 1.3 x 10- 4 m / s .
Thus, the average drift speed is about 0.13 mm/s.