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A metallic element has a cubic lattice. ...

A metallic element has a cubic lattice. Each edge of the unit cell is 2Å. The density of the metal is 2.5 g `cm^(-3)`.The unit cells in 200g of the metal are

A

`1xx10^24`

B

`1xx10^20`

C

`1xx10^22`

D

`1xx10^25`

Text Solution

Verified by Experts

The correct Answer is:
D
Number of unit cell `=("mass of metal")/("mass of one unit cell")`
Given, edge length of unit cell = 2Å `= 2xx10^(-8)` cm
Mass of metal = 200 g
Density of metal = `2.5gcm^(-3)`
Volume of unit cell = `("edge length")^3=(2xx10^(-8))^3`
`=8xx10^(-24)`
Mass of one unit cell = volume x density
`=8xx10^(-24) xx 2.5=20xx10^(-24)`
`therefore` number of unit cell in 200 g metal
`=("mass of metal")/("mass of one unit cell")=(200)/(20xx10^(-24))`
`=10xx10^24=1.0xx10^25`
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