An element crystallizes into a structure which may be describes by a cubic type of unit cell having one atom on each corner of the cube and two atoms on one of its diagonals. If the volume of this unit cell is `24xx10^(-24)cm^(3)` and density of element is `7.2g cm^(-3)` . Calculate the number of atoms present in `200g` of element.

Explanation

No. of atoms per unit cell =`8xx1/8+2=3` i.e., Z=3
Volume of the unit cell =`a^3 = 24xx10^(-24) cm^3`
`rho=(ZxxM)/(a^3xxN_0)`
`therefore 7.2=(3xxM)/((24xx10^(-24))xx(6.023xx10^23))` or M=34.69
Thus , 34.69 g of the element have atoms =`6.023xx10^23`
`therefore` 200 g of element will have atoms =`(6.023xx10^23)/34.69xx200=3.4722xx10^24` atoms