The ratio of the radii of the atom to the nucleus is

Options

A. `10^(4) : 1`
B. `10^(-4) : 1`
C. `10^(2) : 1`
D. `10^(3) : 1`

Answer

To solve the question regarding the ratio of the radii of the atom to that of the nucleus, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Structure of an Atom**:
- An atom consists of a nucleus at its center, which contains protons and neutrons (collectively called nucleons), surrounded by electrons in various shells.

2. **Identifying the Sizes**:
- The radius of an atom is typically on the order of \(10^{-10}\) meters.
- The radius of a nucleus is significantly smaller, approximately \(10^{-14}\) meters.

3. **Setting Up the Ratio**:
- We need to find the ratio of the radius of the atom (\(r_{\text{atom}}\)) to the radius of the nucleus (\(r_{\text{nucleus}}\)).
- This can be expressed mathematically as:
\[ \text{Ratio} = \frac{r_{\text{atom}}}{r_{\text{nucleus}}} \]

4. **Substituting the Values**:
- Substitute the known values into the ratio:
\[ \text{Ratio} = \frac{10^{-10}}{10^{-14}} \]

5. **Calculating the Ratio**:
- To simplify the fraction, we can subtract the exponents:
\[ \text{Ratio} = 10^{-10 - (-14)} = 10^{-10 + 14} = 10^{4} \]

6. **Expressing the Result**:
- Therefore, the ratio of the radii of the atom to that of the nucleus is:
\[ \text{Ratio} = 10^{4} : 1 \]

7. **Conclusion**:
- The correct answer is \(10^{4} : 1\).

### Final Answer:
The ratio of the radii of the atom to that of the nucleus is \(10^{4} : 1\).

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