SATHEE: The Solid State - Result Question 23

The Solid State - Result Question 23

####23. 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,

[2008]

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

(b) $\frac{1}{2} a : \sqrt{3} a : \frac{1}{\sqrt{2}} a$

(d) $a : \sqrt{3} a : \sqrt{2} a$

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Solution:

(a) 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 : $a = 2 r$ or $r = \frac{a}{2}$

For body centred cubic :

$a = \frac{4}{\sqrt{3}} r$ or $r = \frac{\sqrt{3}}{4} a$

For face centred cubic :

$a = 2 \sqrt{2} r$ or $r = \frac{1}{2 \sqrt{2}} a$

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

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

The Solid State - Result Question 23

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The Solid State - Result Question 23

Solution:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

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