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To find:
The packing efficiency of pure silicon.
![Check Mark](/static/check-mark.png)
Answer to Problem 18.121QA
Solution:
The packing fraction of
Explanation of Solution
1) Concept:
We are asked to calculate the packing efficiency of pure silicon. Silicon crystallizes in a diamond lattice form, which contains eight atoms in the unit cell. The radius of the unit cell has been provided, which is used to find the volume of atom, and the density is given, which is used to find the density of the unit cell.
The packing efficiency is defined as the percentage of the total volume of the unit cell occupied by the spheres. The volume of the spheres is calculated by
2) Formulae:
i)
ii)
iii)
iv)
3) Given:
i) Radius of
ii) Density of silicon
iii) Number of atoms per unit cell
iv) Molar mass of
v) Avogadro’s number
4) Calculations:
Mass of silicon atoms in unit cell is
From the given density equation, the volume can be calculated as
The volume occupied by
The packing efficiency is
The packing fraction of the
Conclusion:
The packing efficiency of pure silicon is calculated, which shows that there are lots of empty spaces in the unit cell.
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Chapter 18 Solutions
Chemistry: An Atoms-Focused Approach (Second Edition)
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