The Solid State

The Solid State

Question

An element has atomic mass 93 g mol–1 and density 11.5 g cm–3. If the edge
the length of its unit cell is 300 pm, identify the type of unit cell.

Answer

Given,
M= 93 g mol-1
d= 11.5 g cm-3
a = 300 pm = 300 x 10-10 cm = 3 x 10-8
We know that,
straight d space equals space fraction numerator straight Z space straight x space straight M over denominator straight N subscript straight A space straight x space straight a cubed end fraction
straight Z space equals space fraction numerator straight d space straight x space straight N subscript straight A space straight x space straight a cubed over denominator straight M end fraction space equals fraction numerator 11.5 space straight x 6.022 space straight x space 10 to the power of 23 space left parenthesis space 3 straight x 10 to the power of negative 8 end exponent right parenthesis cubed over denominator 93 end fraction
space equals 2.01
The number of atoms present in given unit cells is coming nearly equal to 2. Hence, the given unit cell is body centred cubic unit cell (BCC).

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