Question

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

• A. \(10^1\)
• B. \(10^5\)
• C. \(10^{10}\)
• D. \(10^{15}\)

Answer 1

The Correct Option is D

To understand the relationship between the volume of an atom and the volume of its nucleus, we need to consider the basic structure of the atom. An atom consists of a central nucleus surrounded by electrons. The nucleus itself is made up of protons and neutrons and is extremely small compared to the overall size of the atom.

Let's go through some key points:

• The radius of an atom is typically about \(10^{-10}\) meters.
• The radius of a nucleus is much smaller, approximately \(10^{-15}\) meters.

The volume of a sphere is calculated using the formula:

V = \frac{4}{3} \pi r^3

So, let's compare their volumes. Assume the atom and the nucleus are roughly spherical:

1. The radius of the atom, r_{\text{atom}} \approx 10^{-10} meters.
2. The radius of the nucleus, r_{\text{nucleus}} \approx 10^{-15} meters.
3. Thus, the volume of the atom is: V_{\text{atom}} = \frac{4}{3} \pi (10^{-10})^3\, which simplifies to V_{\text{atom}} \approx 4.18879 \times 10^{-30} cubic meters.
4. For the nucleus, the volume is: V_{\text{nucleus}} = \frac{4}{3} \pi (10^{-15})^3\, which simplifies to V_{\text{nucleus}} \approx 4.18879 \times 10^{-45} cubic meters.
5. Now, we calculate the ratio of V_{\text{atom}} to V_{\text{nucleus}}:

\frac{V_{\text{atom}}}{V_{\text{nucleus}}} = \frac{10^{-30}}{10^{-45}} = 10^{15}\

Hence, the volume of the atom is greater than the volume of the nucleus by a factor of about 10^{15}.

Therefore, the correct answer is:

10^{15}