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A compound AB has a cubic structure and ...

A compound AB has a cubic structure and molecular mass 99. Its density is `3*4 g cm^(-3)` . What is the length of the edge of the unit cell?

Text Solution

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Let the edge length of each edge = a cm
Volume of unit cell `= a^3 cm^3`
Density (d) = `3.4 g cm^(-3)`
Number of atoms per unit cell (Z) for simple cubic = 1
Molar mass (M) = 99 g `"mol"^(-1)`
Density , d `= (ZM)/(N_A xx a^3)`
or `a^3 = (ZM)/(d xx N_A) = (1 xx 99)/(3.4 xx 6.02 xx 10^(23)) cm^3`
`= 4.84 xx 10^(-23) cm^3`
`a = 3.64 xx 10^(-8) cm = 364 `pm
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