An element with molar mass `2.7xx10^(-2)` kg per mole forms a cubic unit cell with edge length 405 pm. If its density is `2.7xx10^(3)` , what is the nature of the cubic unit cell ?

Explanation

Edge length = 405 pm = `405 xx 10^(-12) m`
Density of the cell = `2.7 xx 10^(3) kg m^(-3)`
Molar mass = `2.7 xx 10^(-2) kg mol^(-1)`
Now density, `= (Z xx M)/(a^3 xx N_A)`
`2.7 xx 10^(3) kg m^(-3) = (Z xx 2.7 xx 10^(-2) kg mol^(-1))/((405 xx 10^(-12)m)^(3) xx (6.022 xx 10^(23) mol^(-1)))`
`:. Z = ((2.7 xx 10^(3) kg m^(-3)) xx (405 xx 10^(-12) m)^(3) xx (6.022 xx 10^(23) mol^(-1)))/(2.7 xx 10^(-2) kg mol^(-1))`
`= 4.0`
Since the unit cell contains 4 atoms, it is cubic close packed structure , ccp .