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Lithium metal crystallizes in a body centred cubic crystal. If the length of the side of the unit cell of lithium is 351 pm, the atomic radius of lithium will be
A
300.5 pm
B
240.8 pm
C
151.8 pm
D
75.5 pm
Detailed Solution
In a body-centred cubic unit cell the atoms touch along the body diagonal.
Body diagonal = $\sqrt{3}a$, and it contains corner atom radius + diameter of the central atom + corner atom radius = 4r
$4r = \sqrt{3}a$, so $r = \frac{\sqrt{3}a}{4}$
$r = \frac{1.732\times351}{4}$
r = 151.98 pm, i.e., about 151.8 pm among the given choices
Body diagonal = $\sqrt{3}a$, and it contains corner atom radius + diameter of the central atom + corner atom radius = 4r
$4r = \sqrt{3}a$, so $r = \frac{\sqrt{3}a}{4}$
$r = \frac{1.732\times351}{4}$
r = 151.98 pm, i.e., about 151.8 pm among the given choices