If `r` is the radius of the octahedral voids and `R` is the radius of the atom in close packing,then `:`

Options

A. `(R)/(r)=9.1`
B. `(R)/(r)=3.22`
C. `(R)/(r)=2.41`
D. `(R)/(r)=4.67`

Explanation

To solve the problem of finding the relationship between the radius of octahedral voids (denoted as `r`) and the radius of the atoms in close packing (denoted as `R`), we can follow these steps:

### Step-by-Step Solution:

1. **Understanding Octahedral Voids**:
In a close-packed structure, octahedral voids are formed between atoms. The radius of these voids is denoted as `r`, while the radius of the atoms that occupy the lattice positions is denoted as `R`.

2. **Known Ratio**:
It is established that the ratio of the radius of the octahedral voids to the radius of the atoms in close packing is a constant value. This ratio is given by:
\[ \frac{r}{R} = 0.414 \]

3. **Finding the Inverse Ratio**:
To find the relationship between `R` and `r`, we can rearrange the equation:
\[ \frac{r}{R} = 0.414 \implies r = 0.414R \]

4. **Expressing `R` in terms of `r`**:
To express `R` in terms of `r`, we can manipulate the equation:
\[ R = \frac{r}{0.414} \]

5. **Calculating the Value**:
To find the numerical value of `R` in terms of `r`, we can calculate:
\[ R = 2.414r \]

6. **Conclusion**:
Thus, the final relationship between the radius of the octahedral voids and the radius of the atoms in close packing is:
\[ R = 2.414r \]