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The density of aluminium (atomic mass = ...

The density of aluminium (atomic mass = 27) is 2700 kg `m^(-3)`. If Al has feestructure, calculate its atomic radius.

Text Solution

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The correct Answer is:
`1.432 xx 10^(-10)` m
`d=(Z xx M)/(N_A xx a^3)`
For fcc unit cell, Z=4, `N_A = 6.023 xx 10^(23)`, M = 27, `d = 2700 kg m^(-3)`, `2700 kg m^(-3) = (4xx27xx10^(-3)kg)/(6.023 xx 10^(23) xx a^3)`
`a^3=(4 xx 27 xx 10^(-3) kg)/(2700 kg m^(-3) xx 6.023 xx 10^(23))` or `a = 4.05 xx 10^(-10)` m
For fcc structure, `r =(a)/(2sqrt2)= (4.05 xx 10^(-10) m)/(2 xx 1.414) = 1.432 xx 10^(-10)` m
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