Question

The number of vacancies per cm\(^3\) in a BCC iron crystal having density of 7.87 g/cm\(^3\) and lattice parameter of \(2.866 \times 10^{-8} \, \text{cm}\) is:

• A. Vacancies/cm\(^3\) = \(1.23 \times 10^2\)
• B. Vacancies/cm\(^3\) = \(1.23 \times 10^2\)
• C. Vacancies/cm\(^3\) = \(1.23 \times 10^3\)
• D. Vacancies/cm\(^3\) = \(1.23 \times 10^8\)

Hint:

For BCC structures, remember that there are 2 atoms per unit cell. This directly impacts the vacancy calculation.

Answer 1

The Correct Option is A

The number of vacancies in a BCC iron crystal can be calculated using the formula:
\[n = \frac{\text{density} \times N_A}{\text{atomic weight} \times a^3 \times 2}\]
where \(N_A\) is Avogadro's number, the density is given, and \(a\) is the lattice parameter.
Substituting the values:
\[n = \frac{7.87 \times 6.022 \times 10^{23}}{55.85 \times (2.866 \times 10^{-8})^3 \times 2} \approx 1.23 \times 10^2 \, \text{vacancies/cm}^3\]