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A metallic element 'X' has cubic lattic....

A metallic element 'X' has cubic lattic. Each edge of the unit cell is `2.0Å` and its density is 2.5 `g cm^(-3)`. Number of atoms in 200g of the metal are `:`

A

`1 xx 10^(20)`

B

`1 xx 10^(22)`

C

`1 xx 10^(24)`

D

`1 xx 10^(25)`

Text Solution

Verified by Experts

The correct Answer is:
D
Volume of unit cell `= ( 2.0 xx 10^(-8) cm )^(3)`
`= 8 xx 10^(-24) cm^(3)`
Density `= 2.5 g cm^(-3)`
Mass of unit cell `= 8 xx 10^(-24) xx 2.5 `
`= 20 xx 10^(-24) g `
No. of unit cells in 200g `= ( 200)/( 20 xx 10^(-24))`
`= 1 xx 10^( 25)`
Since metallic element has simple cubic lattice, number of atoms in a unit cell =1
No. of atoms in 200g of metal
`=1 xx 10^(25) xx 1 `
`= 1 xx 10^(25) ` atoms
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