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An element crystallized in fcc lattice a...

An element crystallized in fcc lattice and edge length of unit cell is 400 pm. If density of unit cell is 11.2 `g cm^(-3)`, then atomic mass of the element is

A

`215.6 g mol^(-1)`

B

`431.2 g mol^(-1)`

C

`107.8 g mol^(-1)`

D

`98.6 g mol^(-1)`

Text Solution

Verified by Experts

The correct Answer is:
C
Edge length of unit cell, a = 400 pm
`= 400 xx 10^(-10) cm`
Density = 11.2 `g cm^(-3)`
Z = 4 ( for fcc )
`d = ( Z xx M )/( a^(3) xx N_(O))`
`11.2 = ( 4 xx M )/( ( 400 xx 10^(-10))^(3) xx ( 6.022 xx 10^(23)))`
or `M = ( 11.2 xx ( 400 xx 10^(-10))^(3) xx ( 6.022xx 10^(23)))/( 4)`
`= 107.8 g mol^(-1)`
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