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A metal has a fcc lattice.The edge lengt...

A metal has a fcc lattice.The edge length of the unit cell is `404` pm ,the density of the metal is `2.72g cm^(-3)` . The molar mass of the metal is `(N_(A)`, Avorgadro's constant `=6.02xx10^(23)mol^(-1))`

A

`40 gmol^(-1)`

B

`30gmol^(-1)`

C

`27gmol^(-1)`

D

`20gmol^(-1)`

Text Solution

Verified by Experts

The correct Answer is:
C
Given , cell is fcc , so Z= 4
Edge length , a = 404 pm `=4.04xx10^(-8) cm`
Density of metal , d= 2.72 g `cm^(-3)`
`N_A= 6.02xx10^23mol^(-1)`
Molar mass of the metal , M=?
We know that density , (d) `=(ZxxM)/(a^3.N_A)`
`therefore M=(d.a^3.N_A)/(Z) = (2.72xx(0.04xx10^(-8))^3xx6.02xx10^23)/(4)`
`=27gmol^(-1)`
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