The \(Cu\) metal crystallizes into fcc lattice with a unit cell length of \(361\, \ pm\). The radius of the copper atom is :
Answer & explanation
Correct answer: option 1
The correct answer is option 1. \(127\, \ pm\)
To find the radius of the copper atom (\(r_{Cu}\)) in the face-centered cubic (fcc) lattice, we can use the formula relating the lattice parameter (\(a\)) and the atomic radius (\(r\)):
\(a = 2 \sqrt{2} \times r\)
Given that the unit cell length (\(a\)) is \(361 \, pm\), we can rearrange the formula to solve for \(r_{Cu}\):
\(r_{Cu} = \frac{a}{2 \sqrt{2}}\)
\(r_{Cu} = \frac{361 \, pm}{2 \sqrt{2}}\)
\(r_{Cu} ≈ \frac{361 \, pm}{2 \times 1.414}\)
\(r_{Cu} ≈ \frac{361 \, pm}{2.828}\)
\(r_{Cu} ≈ 127.68 \, pm\)
Rounding off, the radius of the copper atom (\(r_{Cu}\)) is approximately \(127 \, pm\).
So, the correct answer is option 1. \(127 \, pm\).