AP Physics 1 Questions on Mass Defect and Binding Energy

📚 Quick Study Guide

• ⚛️ Mass defect is the difference between the mass of a nucleus and the sum of the masses of its constituent nucleons (protons and neutrons).
• 🤝 Binding energy is the energy required to separate a nucleus into its constituent nucleons. It's equivalent to the mass defect via $E=mc^2$.
• 📏 The mass defect, $\Delta m$, is calculated as $\Delta m = (Z m_p + N m_n) - m_{nucleus}$, where $Z$ is the number of protons, $N$ is the number of neutrons, $m_p$ is the mass of a proton, $m_n$ is the mass of a neutron, and $m_{nucleus}$ is the mass of the nucleus.
• 💡 Binding energy, $E_b$, is calculated as $E_b = \Delta m c^2$, where $c$ is the speed of light ($3 \times 10^8$ m/s).
• ⚡ Common units include atomic mass units (amu) for mass and MeV (megaelectronvolts) for energy. 1 amu is approximately 931.5 MeV/$c^2$.

🧪 Practice Quiz

1. A nucleus is composed of 8 protons and 8 neutrons. The mass of the nucleus is slightly less than the sum of the masses of its individual protons and neutrons. This difference in mass is known as:
   1. Mass excess
   2. Binding energy
   3. Mass defect
   4. Nuclear force
2. What is the primary reason for the existence of mass defect in a nucleus?
   1. Electromagnetic repulsion between protons
   2. Conversion of mass into energy to bind the nucleus
   3. Loss of particles during nuclear fusion
   4. Increase in nuclear volume
3. Which of the following equations correctly relates mass defect ($\Delta m$) to binding energy ($E_b$)?
   1. $E_b = \frac{\Delta m}{c^2}$
   2. $E_b = \Delta m c$
   3. $E_b = \Delta m c^2$
   4. $E_b = \sqrt{\Delta m c}$
4. The binding energy per nucleon is a measure of:
   1. The total energy of the nucleus
   2. The stability of the nucleus
   3. The number of neutrons in the nucleus
   4. The size of the nucleus
5. If the mass defect for a nucleus is 0.03 amu, what is the approximate binding energy (in MeV)?
   1. 0.03 MeV
   2. 931.5 MeV
   3. 27.9 MeV
   4. 9.315 MeV
6. Which force is overcome by the binding energy of a nucleus?
   1. Gravitational force
   2. Weak nuclear force
   3. Electromagnetic force
   4. Strong nuclear force
7. As the mass number of a nucleus increases, the binding energy per nucleon generally:
   1. Increases continuously
   2. Decreases continuously
   3. Increases to a maximum, then decreases
   4. Remains constant