What is the ratio of volume of atom of the volume of nucleus?

Options

A. `10^(10)`
B. `10^(15)`
C. `10^(20)`
D. `10^(25)`

Explanation

To find the ratio of the volume of an atom to the volume of its nucleus, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Shapes**:
Both the atom and the nucleus are approximately spherical in shape. The formula for the volume \( V \) of a sphere is given by:
\[ V = \frac{4}{3} \pi r^3 \]
where \( r \) is the radius of the sphere.

2. **Set Up the Ratio**:
The ratio of the volume of the atom (\( V_{\text{atom}} \)) to the volume of the nucleus (\( V_{\text{nucleus}} \)) can be expressed as:
\[ \frac{V_{\text{atom}}}{V_{\text{nucleus}}} = \frac{\frac{4}{3} \pi r_1^3}{\frac{4}{3} \pi r_2^3} \]
Here, \( r_1 \) is the radius of the atom and \( r_2 \) is the radius of the nucleus.

3. **Cancel Common Factors**:
The \( \frac{4}{3} \pi \) terms cancel out, simplifying the ratio to:
\[ \frac{V_{\text{atom}}}{V_{\text{nucleus}}} = \frac{r_1^3}{r_2^3} \]

4. **Substitute the Radii**:
We know the approximate values of the radii:
- Radius of the atom, \( r_1 = 10^{-10} \) m
- Radius of the nucleus, \( r_2 = 10^{-15} \) m

Substituting these values into the equation gives:
\[ \frac{V_{\text{atom}}}{V_{\text{nucleus}}} = \frac{(10^{-10})^3}{(10^{-15})^3} \]

5. **Calculate the Cubes**:
Calculate the cubes of the radii:
\[ (10^{-10})^3 = 10^{-30} \]
\[ (10^{-15})^3 = 10^{-45} \]

6. **Find the Ratio**:
Now, substitute these values back into the ratio:
\[ \frac{V_{\text{atom}}}{V_{\text{nucleus}}} = \frac{10^{-30}}{10^{-45}} = 10^{-30 + 45} = 10^{15} \]

7. **Conclusion**:
Therefore, the ratio of the volume of the atom to the volume of the nucleus is:
\[ \frac{V_{\text{atom}}}{V_{\text{nucleus}}} = 10^{15} \]

### Final Answer:
The ratio of the volume of an atom to the volume of its nucleus is \( 10^{15} \).