The volume occupied by an atom is greater than the volume of the nucleus by factor of about

Options

A. `10^1`
B. `10^5`
C. `10^10`
D. `10^15`

Explanation

To solve the problem of finding the factor by which the volume occupied by an atom is greater than the volume of the nucleus, we can follow these steps:

### Step 1: Understand the volumes involved
We need to calculate the volume of an atom and the volume of its nucleus. The formulas for the volumes are:
- Volume of an atom \( V_{atom} = \frac{4}{3} \pi r_{atom}^3 \)
- Volume of a nucleus \( V_{nucleus} = \frac{4}{3} \pi r_{nucleus}^3 \)

### Step 2: Assign values to the radii
Typically, the radius of an atom is about \( r_{atom} = 10^{-10} \) meters, and the radius of a nucleus is about \( r_{nucleus} = 10^{-15} \) meters.

### Step 3: Calculate the volumes
Using the formulas:
1. Volume of the atom:
\[ V_{atom} = \frac{4}{3} \pi (10^{-10})^3 = \frac{4}{3} \pi (10^{-30}) \text{ m}^3 \]

2. Volume of the nucleus:
\[ V_{nucleus} = \frac{4}{3} \pi (10^{-15})^3 = \frac{4}{3} \pi (10^{-45}) \text{ m}^3 \]

### Step 4: Find the ratio of the volumes
Now, we need to find the ratio of the volume of the atom to the volume of the nucleus:
\[ \frac{V_{atom}}{V_{nucleus}} = \frac{\frac{4}{3} \pi (10^{-30})}{\frac{4}{3} \pi (10^{-45})} \]
The \( \frac{4}{3} \pi \) cancels out:
\[ \frac{V_{atom}}{V_{nucleus}} = \frac{10^{-30}}{10^{-45}} \]

### Step 5: Simplify the ratio
Using the properties of exponents:
\[ \frac{10^{-30}}{10^{-45}} = 10^{-30 + 45} = 10^{15} \]

### Conclusion
Thus, the volume occupied by an atom is greater than the volume of the nucleus by a factor of \( 10^{15} \).

### Final Answer
The factor by which the volume occupied by an atom is greater than the volume of the nucleus is \( 10^{15} \).

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