Home › MCQs › EEJ MAIN Chemistry › Question #7138
Back to Questions
EEJ MAIN Chemistry QUESTION #7138
Question 1
Sodium metal forms a body-centered cubic (BCC) lattice with a unit cell edge length of $4.29\text{ \AA}$. Calculate the approximate radius of a sodium atom.
  • $1.86\text{ \AA}$✔️
  • $3.22\text{ \AA}$
  • $5.72\text{ \AA}$
  • $0.93\text{ \AA}$
Correct Answer Explanation
In a body-centered cubic (BCC) lattice, the atoms touch along the body diagonal. The relationship between the edge length ($a$) and the radius ($r$) is given by $\sqrt{3}a = 4r$.
Substituting the values:
$r = \frac{\sqrt{3} \times 4.29}{4} \approx \frac{1.732 \times 4.29}{4} \approx 1.857\text{ \AA}$. Thus, the radius is approximately $1.86\text{ \AA}$.