Question

If the lattice parameter of Si is $5.43$ $\mathring{A}$ and the mass of Si atom is $28.08\times 1.66\times {10}^{-27}$ kg, the density of silicon in kg m${}^{-3}$ is:

[Given: Silicon has a diamond cubic structure.]

• A. $2330$
• B. $1115$
• C. $3445$
• D. $1673$

Answer 1

The correct option is A $2330$

SInce Si has diamond cubic structure, its unit cell contains $8$ atoms.
Density $=\frac{\text{Mass}}{\text{Volume}}$
Mass $=8\times 28.08\times 1.66\times {10}^{-27}=3.73\times {10}^{-25}$ kg
Volume $=(5.43\times {10}^{-10}{)}^3=1.6\times {10}^{-28}$ m${}^3$
Density $=\frac{3.73\times {10}^{-25}}{1.6\times {10}^{-28}}=2330$ kg m${}^{-3}$