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"`

Answer 1

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"`