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Question
An element has a body centered cubic (bcc) structure with a cell edge of 288 pm. The atomic radius is ______.
Options
`sqrt 3/4 xx 288 "pm"`
`sqrt 2/4 xx 288 "pm"`
`4/sqrt3 xx 288 "pm"`
`4/sqrt 2 xx 288 "pm"`
MCQ
Fill in the Blanks
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Solution
An element has a body centered cubic (bcc) structure with a cell edge of 288 pm. The atomic radius is `bbunderline(sqrt 3/4 xx 2 "pm")`.
Explanation:
Edge length a = 288 pm
In a BCC structure, atoms touch along the body diagonal, and the relationship between edge length and atomic radius r is `sqrt 3 a = 4 r`
⇒ r = `sqrt 3/4 a`
⇒ r = `sqrt 3/4 xx 288 "pm"`
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