Question

Calculate the number density of mobile electrons in Ag (density 10.5 g/cm3 ) assuming one free electron per atom. Compare your answere with the experimental value, 5.86 x 10²⁸ m^-3 .

Answer 1

Given that
The density of silver = 10.5 g / cm3
= 10.5 g * 106 g/m3 (since 1 cm = 10-2 m)
That indicates 10.5 g * 106 g of siver present in one cubic meter
We know that
The atomic mass of silver = 107.87 g/mol
The number of moles of silver per cubic meter = {10.5 g * 106 g/m3 } / 107.87 g/mol
= 9.73*104 mol/m3
One mol of silver contains 6.022*1023 silver atoms
∴ Number of silver atoms per cubic meter = 9.73*104 mol/m3 * 6.022*1023 atoms /mol
= 5.86*1028 atoms /m3
Each silver atom possesses one free electron
∴ The number of free electrons per cubic meter for silver = 5.86*1028 electrons /m3