The volume of nucleus is about :

Options

A. `10^(-4)` times to that of an atom
B. `10^(-15)` times to that of an atom
C. `10^(-5)` times to that of an atom
D. `10^(-10)` times to that of an atom

Answer

To find the volume of the nucleus in relation to the volume of the atom, we can follow these steps:

### Step 1: Understand the formula for the volume of a sphere
The volume \( V \) of a sphere is given by the formula:
\[ V = \frac{4}{3} \pi r^3 \]
where \( r \) is the radius of the sphere.

### Step 2: Calculate the volume of the nucleus
Assuming the nucleus is spherical, we need to find its volume using its radius. The radius of the nucleus is approximately \( 10^{-13} \) meters.

Using the formula:
\[ V_n = \frac{4}{3} \pi (r_n)^3 \]
Substituting \( r_n = 10^{-13} \):
\[ V_n = \frac{4}{3} \pi (10^{-13})^3 \]
Calculating \( (10^{-13})^3 \):
\[ (10^{-13})^3 = 10^{-39} \]
Thus,
\[ V_n = \frac{4}{3} \pi (10^{-39}) \]

### Step 3: Calculate the volume of the atom
Next, we calculate the volume of the atom. The radius of the atom is approximately \( 10^{-8} \) meters.

Using the same volume formula:
\[ V_a = \frac{4}{3} \pi (r_a)^3 \]
Substituting \( r_a = 10^{-8} \):
\[ V_a = \frac{4}{3} \pi (10^{-8})^3 \]
Calculating \( (10^{-8})^3 \):
\[ (10^{-8})^3 = 10^{-24} \]
Thus,
\[ V_a = \frac{4}{3} \pi (10^{-24}) \]

### Step 4: Find the ratio of the volume of the nucleus to the volume of the atom
Now, we need to find the ratio \( \frac{V_n}{V_a} \):
\[ \frac{V_n}{V_a} = \frac{\frac{4}{3} \pi (10^{-39})}{\frac{4}{3} \pi (10^{-24})} \]
The \( \frac{4}{3} \pi \) cancels out:
\[ \frac{V_n}{V_a} = \frac{10^{-39}}{10^{-24}} = 10^{-39 + 24} = 10^{-15} \]

### Conclusion
The volume of the nucleus is \( 10^{-15} \) times the volume of the atom. Therefore, the answer is:
\[ \text{Volume of nucleus} = 10^{-15} \times \text{Volume of atom} \]