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The density of copper metal is ` 8.95 " g cm"^(-3)` . If the radius of copper atom is 127.8 pm, is the copper unit cell a simple cubic, a body- centred cubic or a face- centred cubic? ( Given At. Mass of Cu= 63.54 g ` " mol"^(-1) and N_(A) = 6.02 xx 10^(23) " mol"^(-1))` |
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Answer» If copper atom were simple cubic, a =2 r=2 ` xx` 127.8 pm = 256. 6 pm ` Z = 1 : P = ( Z xx M)/( a^(3) xx N_(0)) = ( 1xx 63.54 " g mol"^(-1))/ (( 255.6 xx 10^(-10) "cm") ^(3) xx ( 6.02 xx 10^(23) mol^(-1)) ) = 6.34 " g cm" ^(-3)` Actual ` p = 8.95 " g cm"^(-3)` Hence, copper atom is not simple cubic. If copper atom were body - centred. ` a = (4r)/(sqrt3) = ( 4xx 127.8)/(1.732) " pm" = 295.15` pm ` Z=2 , p = ( Z xx M)/( a^(3) xx N_(0)) = ( 2 xx 63.54 " g mol"^(-1))/ ( ( 295. 15 xx 10^(-10) "cm") xx 6.02 xx 10^(23) "mol" ^(-1)) = 8.21 " g cm"^(-3)` Hence, copper atom is not body- centred. If copper atom were face - centred. `a= 2sqrt2r = 2xx 1.414 xx 127.8 "pm" = 361 . 4"pm"` `Z=4 , p = ( Z xx M)/(a^(3)xxN_(0)) = ( 4xx63.54" g mol"^(-1))/((361.4xx10^(-10) "cm") xx 6.02 xx 10^(23) "mol" ^(-1))= 8.94 " g cm" ^(-3)` Hence, copper is face - centred cubic. |
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