Ratio of the volume of a nucleus to the volume of its atom is around

Options

A. `10^2`
B. `10^-2`
C. `10^(-12)`
D. `10^(-16)`

Answer

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

### Step 1: Understand the radii of the nucleus and the atom
- The radius of the nucleus (\(r_n\)) is approximately \(10^{-15}\) meters.
- The radius of the atom (\(r_a\)) is approximately \(10^{-10}\) meters.

### Step 2: Calculate the volume of the nucleus
- The volume of a sphere is given by the formula:
\[ V = \frac{4}{3} \pi r^3 \]
- For the nucleus:
\[ V_n = \frac{4}{3} \pi (r_n)^3 = \frac{4}{3} \pi (10^{-15})^3 \]
- Simplifying this:
\[ V_n = \frac{4}{3} \pi (10^{-45}) \text{ cubic meters} \]

### Step 3: Calculate the volume of the atom
- For the atom:
\[ V_a = \frac{4}{3} \pi (r_a)^3 = \frac{4}{3} \pi (10^{-10})^3 \]
- Simplifying this:
\[ V_a = \frac{4}{3} \pi (10^{-30}) \text{ cubic meters} \]

### Step 4: Calculate the ratio of the volumes
- The ratio of the volume of the nucleus to the volume of the atom is:
\[ \text{Ratio} = \frac{V_n}{V_a} = \frac{\frac{4}{3} \pi (10^{-45})}{\frac{4}{3} \pi (10^{-30})} \]
- The \( \frac{4}{3} \pi \) terms cancel out:
\[ \text{Ratio} = \frac{10^{-45}}{10^{-30}} = 10^{-15} \]

### Conclusion
- The ratio of the volume of a nucleus to the volume of its atom is approximately \(10^{-15}\).