Question

Lithium forms body-centered cubic structure. The length of the side of its unit cell is $351\mathrm{pm}$. What will be the Atomic radius of lithium?

• A. $152\mathrm{pm}$
• B. $175\mathrm{pm}$
• C. $240\mathrm{pm}$
• D. $300\mathrm{pm}$

Answer 1

The correct option is A

$152\mathrm{pm}$

Explanation for the correct Option:

Option(A): $152\mathrm{pm}$

Step 1: Given data:

Given that, In a body-centered cubic (bcc) structure of Lithium, Edge length (a) = $351\mathrm{pm}$
Step 2: Formula giving the relation between radius and edge length:

We know, radius $=\frac{\sqrt{3}}{4}\mathrm{a}$
(Where, $\mathrm{a}=\mathrm{edge}\mathrm{length}\mathrm{of}\mathrm{a}\mathrm{unit}\mathrm{cell}$)
Step 3: calculation of radius by using the formula:

Hence, the radius of the bcc structure can be calculated as:
$$\begin{gathered} \mathrm{r}=\frac{\sqrt{3}}{4}\times 351 \\ \Rightarrow \mathrm{r}=\sqrt{3}\times 87.75 \\ \Rightarrow \mathrm{r}=152\mathrm{pm} \end{gathered}$$
Hence, the atomic radius of Lithium will be $152\mathrm{pm}$.