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Gunjan Brock Pandit
Asked: 2022-11-08T21:19:31+05:30 In:

If a metal crystallises in a face-centred cubic structure with metallic radius of 25 pm, the number of unit cells in `1 cm^(3)` of lattice is :
A. `2.828 xx 10^(28)`
B. `1.414xx10^(28)`
C. `1.414xx10^(24)`
D. `2.828xx 10^(24)`

If a metal crystallises in a face-centred cubic structure with metallic radius of 25 pm, the number of unit cells in `1 cm^(3)` of lattice is :
A. `2.828 xx 10^(28)`
B. `1.414xx10^(28)`
C. `1.414xx10^(24)`
D. `2.828xx 10^(24)`
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  1. Correct Answer – D
    `asqrt(2)=4r`
    `axx 1.414=4xx25`
    `a=70.72` pm `=70.72xx10^(-10)` cm
    Volume of one unit cell `=a^(3)=(70.72xx10^(-10))^(3)`
    `=3.536xx10^(-25) cm^(3)`
    Number of unit cells in `1 cm^(3)` lattice `=(1)/(3.536xx10^(-25))`
    `=2.828xx10^(24)`

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