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.

Options

A. `3.5xx10^24`
B. `5.7xx10^23`
C. `6.3xx10^20`
D. `1xx10^10`

Answer

A

Explanation

No. of atoms in unit cell=1+2=3
Volume of unit cell = `24xx10^(-24) cm^3`
Density =` 7.2 g cm^(-3)`
`because` Density=`"n x at.wt."/(VxxN_A)`
`therefore 7.2=(3xx at.wt.)/(24xx10^(-24)xx6.023xx10^23)`
`therefore` At. Wt. =34.69
`because` 34.69 g has no. of atoms = `6.023xx10^23`
200 g has no. of atoms = `(6.023xx10^23xx200)/34.69`
`=3.4722xx10^24` atoms `approx 3.5xx10^24` atoms