In an fcc lattice, the atoms are located at the corners and the centers of the faces.
The atoms touch along the face diagonal.
The face diagonal is equal to \(4r\), where \(r\) is the radius of the atom.
The face diagonal is also equal to \(a\sqrt{2}\), where \(a\) is the edge length.
Therefore,
\[
4r = a\sqrt{2}
\]
\[
r = \frac{a\sqrt{2}}{4} = \frac{a}{2\sqrt{2}}
\]
\( a = 200 \) pm \( = 200 \times 10^{-12} \) m
3. Calculate the radius (r):\[ r = \frac{200 \times 10^{-12} \, \text{m}}{2\sqrt{2}} \] \[ r = \frac{100 \times 10^{-12} \, \text{m}}{\sqrt{2}} \] \[ r = \frac{100}{\sqrt{2}} \times 10^{-12} \, \text{m} \] \[ r = \frac{100 \times \sqrt{2}}{2} \times 10^{-12} \, \text{m} \] \[ r = 50\sqrt{2} \times 10^{-12} \, \text{m} \] \[ r = 50 \times 1.414 \times 10^{-12} \, \text{m} \] \[ r = 70.7 \times 10^{-12} \, \text{m} \] \[ r = 7.07 \times 10^{-11} \, \text{m} \]
4. Check the given options:Let's cube the radius: \[ (7.07 \times 10^{-11})^3 = 353.4 \times 10^{-33} \] \[ \sqrt[3]{353.4 \times 10^{-33}} = \sqrt[3]{0.3534 \times 10^{-30}} = \sqrt[3]{0.353} \times 10^{-10} \]
Final Answer:
\( \sqrt[3]{0.353} \times 10^{-10} \) m.
Two statements are given below
Statement I: Benzanamine can be prepared from phthalimide.
Statement II: Benzanamine is less basic than phenyl methanamine.
What are X and Z in the following reaction sequence?
What is Y in the following reaction sequence?
Observe the following set of reactions:
Correct statement regarding Y and B is:
What is X in the following reaction?