Silver froms ccp lattice and `X`-ray studies of its crystals show that the edge length of its unit cell is `408.6` pm. Calculate the density of silver (atomic mass `= 107.9 u`).

Explanation

Since the lattice is ccp , the number of silver atoms per unit cell = z = 4
Molar mass of silver = `107.9 g mol^(-1) = 107.9 xx 10^(-3) kg mol^(-1)`
Edge length of unit cell = a = 408. 6 pm = 408.6 `xx 10^(-12)`m
Density , d = `(zM)/( a^(3) . N_(A))`
`= (4 xx (107.9 xx 10^(-3) kg mol^(-1)))/((408.6 xx 10^(-12) m)^(3) (6.022 xx 10^(23) mol^(-1)))`
`=10.5 xx 10^(3) kg m^(-3)`
`= 10.5 g cm^(3)`.