Answer to Question #217282 in Mechanics | Relativity for Ateufack Zeudom

Question

A current, I=200A is passed through a copper conductor of cross section: S=1cm². We suppose that all the atoms are transformed into Cu²⁺ ions. The density of copper is given by 8.9x10³kg/m³ ; ( atomic mass is M=0.0635kg/mol and the Avogadro number is N=6.22x10³ mol^-1. Calculate the number of electrons per m³:

Answer 1

Gives $I=200A\\S=1cm^2M=8.9\times10^3kg/m^3\\M=0.0635kg/mol\\N=6.23\times10^{23}mol^{-1}\\cu^{2+},n=2$

$\frac{N}{N_A}=\frac{m}{M}$

$n=\frac{N}{V}$

$n=\frac{m}{M}\times\frac{N_A}{V}$

$n=\frac{N_A}{V}\times d$

Electron density

$$n=\frac{6.22\times10^{23}\times8.9\times10^3}{0.0635}=8.72\times10^{28}m^{-3}$$

Now as such atom contribution two electron the number of electron per unit volume

$n_e=2\times n$

$$n_e=2\times8.72\times10^{28}=17.4\times10^{28}m^{-3}$$