Question

Calculate the number of free electrons per cubic meter for silver, assuming that there are 1.3 free electrons per silver atom. The electrical conductivity and density for Ag are 6.8 × 107(Ω.m)–1and 10.5 g/cm3, respectively.

Answer 1

Answer : The number of free electrons per cubic meter for silver are
`7.62* 10^(28)m^(-3)`

Explanation :

To calculate the number of free electrons per cubic meter for silver by using the following equation:

`n=1.3* N_(Ag)`

`n=1.3* (\rho_(Ag)* N_A)/(A_(Ag))`

where,

`\rho_(Ag)` = density of Ag =
`10.5g/cm^3`

`N_A` = Avogadro's number =
`6.022* 10^(23)atoms/mol`

`A_(Ag)` = 107.87 g/mol

Now put all the given values in the above formula, we get:

`n=1.3* (\rho_(Ag)* N_A)/(A_(Ag))`

`n=1.3* ((10.5g/cm^3)* (6.022* 10^(23)atoms/mol))/(107.87g/mol)`

`n=7.62* 10^(22)cm^(-3)`

`n=7.62* 10^(28)m^(-3)`

conversion used :
`1cm^(-3)=10^6m^(-3)`

Therefore, the number of free electrons per cubic meter for silver are
`7.62* 10^(28)m^(-3)`