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If 'a' stands for the edge length of the...

If 'a' stands for the edge length of the cubic system, sc,bcc,and fcc. Then the ratio of radii of spheres in these system will be respectively.

A

`(1/2a : (sqrt3)/2 : (sqrt2)/2 a)`

B

`(sqrt(1)a : sqrt(3)a : sqrt(2)a)`

C

`(1/2a : (sqrt3)/4 a : 1/(2sqrt2)a)`

D

`(1/2 a : sqrt(3)a : 1/(sqrt2)a)`

Text Solution

Verified by Experts

The correct Answer is:
C
`sc implies 2r = a implies r = a/2`
`bcc implies 4r = sqrt(3)a implies r = (sqrt(3)a)/(4)`
`fcc implies 4p = sqrt(2)a implies r = (sqrt(2)a)/4 = a/(2sqrt(2))`
`(a/2):((sqrt(3)a)/(4)) : (a/(2sqrt(2)))`
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