Problem Solutions For Introductory Nuclear Physics By Kenneth S. Krane !new! May 2026

Problem 1.1: Krane, Chapter 1

Verify that the mass defect of the deuteron $\Delta M_d$ is approximately 2.2 MeV.

Step 1: Translate the problem into nuclear quantities.

List what is given (half-life, Q-value, spin-parity, cross-section). Identify what is asked (radius, transition rate, angular distribution). Write down relevant constants (ħc = 197.3 MeV·fm, 1 u = 931.5 MeV/c², etc.).

3. Student-Created Solution Archives (Use with Caution)

Websites like Physics Forums, Chegg, Course Hero, and Slader (now part of Quizlet) host user-uploaded solutions. Quality varies wildly: Problem 1

  • Good: Detailed step-by-step reasoning, checking units and physical plausibility.
  • Bad: Numeric answers without derivation, wrong constants, or logic that skips crucial nuclear physics concepts.

Example: For a problem on beta decay Q-values, a poor solution might just state the answer (e.g., “4.2 MeV”). A good solution will show: ( Q = [m(^14C) - m(^14N)]c^2 ), then plug in atomic mass excesses from the appendix, convert to MeV, and discuss why the daughter nucleus is left in an excited state.

The Unofficial Solutions: A Tiered Guide

Students hunting for solutions will find three primary tiers of resources. Understanding the quality and legitimacy of each is critical.

Step 3: Calculate the mass defect

$\Delta M_d = M_p + M_n - M_d = 938.27 + 939.57 - 1875.61 = 2.23$ MeV. Example: For a problem on beta decay Q-values,

How to Ethically Use a Solutions Manual

You have found a solution for Krane’s problem 6.15 (the deuteron photodisintegration). Now what?

DO NOT:

  • Copy it directly into your homework.
  • Memorize the steps without understanding the physics.
  • Skip the derivation because "the answer is in the manual."

DO THIS INSTEAD:

  1. Cover the solution. Read the problem statement only.
  2. Attempt the problem for 20–30 minutes. Write down where you get stuck (e.g., "I don’t know how to set up the integral for the cross-section").
  3. Reveal the first line of the solution. Does it match your approach? If not, why?
  4. Close the manual and resume your attempt.
  5. Repeat until you finish. Then compare your final answer.
  6. Write a "lessons learned" note: "I forgot to include the reduced mass in the tunneling probability."

This method, sometimes called active solution usage, transforms a passive crutch into an active tutor.

Classic Problem Examples and Solution Pitfalls

| Problem | Common Mistake | Solution Tip | | :--- | :--- | :--- | | 2.3 – Rutherford scattering impact parameter | Confusing ( \theta ) (scattering angle) with ( \phi ) (azimuthal). | Draw the geometry. ( b = \frac12 \fracZ_1 Z_2 e^2E_\textlab \cot(\theta/2) ). | | 4.8 – Nuclear parity from pion capture | Forgetting that parity is multiplicative, and that the pion is pseudoscalar. | Write ( \pi_i = \pi_\pi \cdot \pi_\texttarget \cdot (-1)^L ). | | 9.3 – Gamma transition multipolarity | Using electric dipole (E1) selection rules for a transition between same-parity states. | ( \Delta \pi = \textno ) for E1? No — E1 requires parity change. | | 13.12 – Reaction threshold energy | Using ( E_\textth = -Q ) for non-relativistic case but forgetting the projectile-target mass factor. | Correct: ( E_\textth = -Q \fracm_\textprojectile + m_\texttargetm_\texttarget ). |

Final Verdict: The Best “Solution” Is a Study Group

No single solutions manual can replace discussing nuclear physics with peers. Krane’s book shines when you argue about why ( ^8Be ) is unbound or why ( ^208Pb ) is doubly magic. Form a study group. Work problems together on a whiteboard. Only then consult written solutions to settle debates. sometimes called active solution usage

Step 5: Compare with experimental data (if available).

Many Krane problems cite actual nuclides (e.g., (^238)U alpha decay, (^60)Co gamma cascade). Look up the evaluated nuclear data from NNDC (Brookhaven National Laboratory) or NuDat. If your solution disagrees with the known half-life or branching ratio, re-examine your assumptions.