The ratio of `r_(n)//r_(0) (r_(n) = "radius of nucleus and "r_(0)"is radius of atom ")`

Options

A. A
B. `A^(1//3)`
C. `A^(2//3)`
D. `A^(3//2)`

Answer

To solve the question regarding the ratio of the radius of the nucleus (Rn) to the radius of the atom (R0), we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Relationship**:
The radius of the nucleus (Rn) is related to the mass number (A) of the nucleus. The formula that describes this relationship is:
\[ R_n = R_0 \cdot A^{1/3} \]
where \( R_0 \) is a constant that represents the radius of an atom.

2. **Substituting Rn in the Ratio**:
We want to find the ratio \( \frac{R_n}{R_0} \). Using the formula from step 1, we can substitute \( R_n \):
\[ \frac{R_n}{R_0} = \frac{R_0 \cdot A^{1/3}}{R_0} \]

3. **Simplifying the Ratio**:
In the equation above, the \( R_0 \) in the numerator and denominator cancels out:
\[ \frac{R_n}{R_0} = A^{1/3} \]

4. **Conclusion**:
Therefore, the ratio of the radius of the nucleus to the radius of the atom is:
\[ \frac{R_n}{R_0} = A^{1/3} \]

### Final Answer:
The ratio \( \frac{R_n}{R_0} \) is \( A^{1/3} \).