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VITEEE 2017 Paper

Section: Chemistry

Question : 50 of 125

Marks: +1, -0

If 'a’ stands for the edge length of the cubic systems : simple cubic, body centred cubic and face centred cubic, then the ratio of radii of the spheres in these systems will be respectively,

$\frac{1}{2}$ a : $\frac{\sqrt{3}}{4}$ a : $\frac{1}{2\sqrt{2}}$ a
$\frac{1}{2}$ a : $\sqrt{3}$ a : $\frac{1}{\sqrt{2}}$ a
$\frac{1}{2}$ a : $\frac{\sqrt{3}}{2}$ a : $\frac{\sqrt{3}}{2}$ a
1a : $\sqrt{3}$ a : $\sqrt{2}$ a

Validate

Solution:

Following generalization can be easily derived for various types of lattice arrangements in cubic cells between the edge length (a) of the cell and r the radius of the sphere.

For simple cubic : a = 2r or r =

\frac{a}{2}

For body centred cubic :

a =

\frac{4}{\sqrt{3}}

r or r =

\frac{\sqrt{3}}{4}

For face centred cubic :

a =

2\sqrt{2}r

or r =

\frac{1}{2\sqrt{2}}

Thus the ratio of radii of spheres for these will be simple: bcc: fcc

\frac{1}{2}

a :

\frac{\sqrt{3}}{4}

a :

\frac{1}{2\sqrt{2}}

option (a) is correct answer.

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