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Lithium forms body centred cubic structure. The length of the side of its unit cell is $$351$$ pm. Atomic radius of the lithium will be:
For lithium the crystal structure is body-centred cubic (bcc).
In a bcc unit cell the atoms touch each other along the body diagonal.
Length of the body diagonal = $$\sqrt{3}\,a$$, where $$a$$ is the edge length.
Along this diagonal we have: corner atom (radius $$r$$) + body-centre atom (diameter $$2r$$) + opposite corner atom (radius $$r$$).
Therefore
$$\sqrt{3}\,a = 4r \qquad -(1)$$
Given $$a = 351\;\text{pm}$$, substitute in equation (1):
$$r = \frac{\sqrt{3}}{4}\,a = \frac{1.732}{4} \times 351\;\text{pm}$$
$$r = 0.433 \times 351\;\text{pm} \approx 151.9\;\text{pm}$$
Rounded to the nearest whole number, the atomic radius of lithium is $$152\;\text{pm}$$.
Hence, Option D which is: $$152\;\text{pm}$$.
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