🔖 Topics

  • Nuclear physics vocabulary
  • The mass defect
  • The strong force
  • Binding energy
  • Types of nuclear radiation

🎯 Objectives

  • Learn some of the vocabulary terms used in nuclear physics
  • Calculate the mass defect in a nucleus and explain how it relates to binding energy.
  • Describe some of the major modes of nuclear radiation (i.e. alpha decay, beta decay, gamma decay, and electron capture).

📋 Sequence

  • Set the stage: Two blobs fly towards each other at relativistic speed and stick together. What is the change in mass of the blobs?
  • Vocabulary
    • Nucleon - a particle that is found in the nucleus of an atom (i.e. a proton or a neutron)
    • Nucleon number (A) - the number of protons and neutrons in a nucleus, also called the mass number
    • Atomic number (Z) - the number of protons in an atom
    • Isotope - an atom with a specific number of protons, but different masses due to different numbers of neutrons
    • Atomic mass unit - 1/12 the mass of a neutral \( ^{12}C \) atom. \(1 \: u = 1.66 \times 10^{-27} \: kg \). Nucleons have a mass approximately equal to 1 u.
  • Radius of a nucleus:
    • \( r = r_o A^{1/3} \) where \(r_o \approx 1.2 :fm \)
  • Coulomb force between two protons:
    • \( F = kq^2/r^2 = (9e9)(1.6 \times 10^{-19})^2/(1 \times 10^{-15})^2 \approx 230 \: N \)
    • \( F = ma \Rightarrow a = (230 \: N)/(1.67 \times 10^{-27} \: kg) = 1.38 \times 10^{29} \: m/s^2 \)
    • Why doesn’t the universe just explode and everything die?
  • Strong force
    • There is a very short range force that holds nucleons together
    • Comparison of strong force to electromagnetism / gravity
    • Where does the strong force come from?
  • The mass deficit
    • The mass of Z protons and N neutrons is not equal to the measured mass of a nucleus
    • Example problem: What is the binding energy of the \( ^{14}N \) nucleus?
  • The binding energy curve
  • How nuclei become more stable?
    • Disintegration energy - the amount of rest energy that gets turned into other forms of energy
    • Alpha decay
    • Beta decay
    • Electron capture
    • Gamma decay
    • Other modes

🖥️ Animations, Simulations, Activities

N/A

📝 Practice Problems

  1. What is the binding energy of deuteron (\(^2H\)). The mass of a deuteron nucleus is 2.013553 u. Hint: it is helpful to do the calculation in terms of atomic mass units instead of kilograms. Then, you can convert units using \(1 \: u c^2 = 931.494 \: MeV\)
  2. Radon-222 is a radioactive gas that can sometimes be produced by the alpha decay of a parent nuclide. What is the parent nuclide?
  3. Write out the reaction when sodium-22 decays by electron capture. Hint: don’t forget the neutrino!
  4. Write out the reaction when sodium-22 decays by emitting a positron. Hint: don’t forget the neutrino!

✅ Partial Solutions

  1. 2.225 MeV

📘 Connected Resources

  • Giambattista, Alan, et al. College Physics With an Integrated Approach to Forces and Kinematics. 5th ed., McGraw-Hill Education, 2020.