Question

The density of copper is 3 3 8.93 10 / kg m . Calculate the number of free electrons per
cubic meter and hence their drift velocity when a current is flowing whose density is 21 / A cm . Take Avogadro’s number as 23 6.022 10 / atoms mole and the molar mass of cupper is 63.55g.

Answer 1

Answer on question #84174, Engineering / Electrical Engineering

The density of copper is 3 3 8.93 10 / kg m. Calculate the number of free electrons per cubic meter and hence their drift velocity when a current is flowing whose density is 21 / A cm. Take Avogadro's number as 23 6.022 10 / atoms mole and the molar mass of copper is 63.55g

Solution

The number of free electron is:

$$n = \frac {N _ {A}}{M} \cdot m = \frac {N _ {A}}{M} \cdot \rho V = \frac {6 . 0 2 2 \cdot 1 0 ^ {2 3} \cdot 8 . 9 3 \cdot 1 0 ^ {3} \cdot 1}{6 3 . 5 \cdot 1 0 ^ {- 3}} = 0. 8 4 7 \cdot 1 0 ^ {2 9} \mathrm {f r e e e l e c t r o n s}$$

Their drift velocity is:

$$v = \frac {I / S}{e \cdot n _ {0}} = \frac {1 0 ^ {4}}{1 . 6 \cdot 1 0 ^ {- 1 9} \cdot 0 . 8 4 7 \cdot 1 0 ^ {2 9}} = 0. 7 3 8 \cdot 1 0 ^ {- 6} \mathrm {m e t e r / s e c}$$

Answer: $n = 0.847 \cdot 10^{29}$ free electrons, $v = 0.738 \cdot 10^{-6}$ meter/sec

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