Question

Given,\[{M^ + }\] Form \[{M_3}{C_{60}}\] where \[C_{60}^{ - 3}\] fulleride (a superconductor) octahedral holes. The radius of \[C_{60}^{ - 3}\] is \[500pm\] . Then the minimum possible radius for \[{M^ + }\] is,
 A.\[307pm\]
 B.\[367pm\]
 C.\[207pm\]
 D.\[500pm\]

Answer 1

Hint: We need to know that the superconductors are the solids which show zero resistance in the presence of low temperature and it flows the electric current. And this is known as superconductivity. And the fullerides are the compounds which contain fullerene anions and it is also known as buckminsterfullerene. It is mainly used as a radical scavenger and antioxidant.

Complete answer:
The minimum possible radius for \[{M^ + }\] is not equal to\[307pm\]. Hence, option (A) is incorrect.
The minimum possible radius for \[{M^ + }\] is not equal to\[367pm\]. Hence, the option (B) is incorrect.
Here, the cation \[{M^ + }\]forms \[{M_3}{C_{60}}\]. And \[C_{60}^{ - 3}\]is the fulleride which is a superconductor. And that is made up of $60$ carbon atoms.
Given, radius of \[C_{60}^{ - 3}\] is equal to \[500pm\]
Therefore, the minimum possible radius for \[{M^ + }\] can be find out by using the equation,
\[\dfrac{{\sqrt 3 }}{4}r\]
Where, r is the radius of \[C_{60}^{ - 3}\]. By substituting the value of radius in above equation, will get,
\[\dfrac{{\sqrt 3 }}{4}r = \dfrac{{\sqrt 3 }}{4}x500 = 207\]
Thus, the minimum possible radius for \[{M^ + }\]is equal to \[207pm\]. Hence, option (C) is correct.
The minimum possible radius for \[{M^ + }\] is not equal to the radius of\[C_{60}^{ - 3}\]. Thus, it is not equal to \[500pm\]. Hence, the option (D) is incorrect.

Note:
We also know that \[C_{60}^{ - 3}\] is a common fullerene and it contains $60$carbon atoms. Here, the \[{M^ + }\] cation is reacting to form the superconductor, which is \[C_{60}^{ - 3}\] fulleride. And it has octahedral holes. Here, every carbon will contain three bonds. And these are dissolves in hydrocarbon solvents. By using the given value, I will get the minimum possible radius for \[{M^ + }\] and it is equal to \[207pm\].