Solved Examples of Nuclear Radius Calculation

📚 Quick Study Guide

• ⚛️ The nuclear radius (R) is related to the mass number (A) of an atom.
• 📏 The empirical formula for nuclear radius is given by: $R = R_0 A^{1/3}$, where $R_0$ is approximately 1.2 fm (femtometers).
• 💡 $R_0$ varies slightly depending on the nucleus, but 1.2 fm is a good approximation.
• 🔢 A is the mass number, representing the total number of protons and neutrons in the nucleus.
• 📝 To calculate R, simply plug in the value of A into the formula.

🧪 Practice Quiz

1. What is the approximate radius of a nucleus with a mass number of 64, given $R_0 = 1.2 \text{ fm}$?
   1. 2.4 fm
   2. 4.8 fm
   3. 9.6 fm
   4. 19.2 fm
2. If the nuclear radius of an atom is 3.6 fm, what is its mass number (approximately)?
   1. 8
   2. 27
   3. 64
   4. 125
3. Which of the following best describes the relationship between nuclear radius (R) and mass number (A)?
   1. $R \propto A$
   2. $R \propto A^2$
   3. $R \propto A^{1/3}$
   4. $R \propto \sqrt{A}$
4. What is the nuclear radius of Helium-4 ($\text{He}^4$), given $R_0 = 1.2 \text{ fm}$?
   1. 1.9 fm
   2. 3.8 fm
   3. 4.8 fm
   4. 6.0 fm
5. If a nucleus has a mass number of 27, what is its approximate radius, given $R_0 = 1.2 \text{ fm}$?
   1. 2.4 fm
   2. 3.6 fm
   3. 4.2 fm
   4. 4.8 fm
6. Consider two nuclei, one with mass number 8 and the other with mass number 216. What is the ratio of their radii?
   1. 1:3
   2. 1:9
   3. 1:27
   4. 1:6
7. What does $R_0$ represent in the nuclear radius formula?
   1. The radius of a neutron
   2. The radius of a proton
   3. An empirical constant
   4. The atomic mass unit