Question

How many times greater is the radius of an atom compared to the radius of its nucleus?

• A. $ 10^2 $ times
• B. $ 10^3 $ times
• C. $ 10^4 $ times
• D. $ 10^5 $ times

Hint:

Although the nucleus contains most of the atom's mass, it occupies only a tiny fraction of the atom’s volume. The atom is mostly empty space occupied by the electron cloud.

Answer 1

The Correct Option is C

Step 1: Understand atomic and nuclear dimensions
The radius of a typical atom is approximately \( 10^{-10} \, \text{m} \).
The radius of a nucleus is given by: \[ R = r_0 A^{1/3} \] where \( r_0 \approx 1.2 \times 10^{-15} \, \text{m} \) and \( A \) is the mass number.
For a typical atom with \( A = 100 \): \[ R_{\text{nucleus}} \approx 1.2 \times 10^{-15} \times 100^{1/3} \approx 1.2 \times 10^{-15} \times 4.64 \approx 5.57 \times 10^{-15} \, \text{m} \] Step 2: Calculate the ratio
\[ \frac{R_{\text{atom}}}{R_{\text{nucleus}}} = \frac{10^{-10}}{5.57 \times 10^{-15}} \approx 1.8 \times 10^4 \approx 10^4 \] So, the radius of an atom is about \( 10^4 \) times greater than the radius of its nucleus. Step 3: Conclusion
The correct answer is: \[ {10^4 \text{ times}} \]