Solution Of Elements Nuclear Physics Meyerhof Upd Updated -

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2. Essential Problem-Solving Toolkit

Before attempting problems, ensure you have the following "cheat sheet" of constants and relations ready. Meyerhof heavily relies on these: Avogadro’s Number ($N_A$) $\approx 6

A. Fundamental Constants

• Avogadro’s Number ($N_A$) $\approx 6.022 \times 10^23$ mol$^-1$
• Speed of light ($c$) $\approx 3.00 \times 10^8$ m/s
• Electron mass ($m_e$) $\approx 0.511$ MeV/c$^2$
• Atomic Mass Unit ($u$) $\approx 931.5$ MeV/c$^2$
• Proton mass ($m_p$) $\approx 938.27$ MeV/c$^2$
• Fine structure constant ($\alpha$) $\approx 1/137$

B. Key Formulas by Topic

Problem 10.5: Compound Nucleus – Resonance Scattering

Given: Neutron scattering on ( ^56Fe ) at E_n=20 keV, resonance width Γ=1 keV, Γ_n=0.5 keV.
Solution:
Cross section: ( \sigma = \frac\pik^2 \frac\Gamma_n \Gamma(E-E_R)^2 + (\Gamma/2)^2 )
At resonance (E=E_R): ( \sigma_max = \frac\pik^2 \frac\Gamma_n\Gamma/2 = \frac2\pik^2 \frac\Gamma_n\Gamma )
For E_n=20 keV, k = √(2mE)/ħ ≈ 0.05 fm⁻¹, so π/k² ≈ 1.26×10³ b.
Thus σ_max = 2×1.26×10³ × (0.5/1) ≈ 1260 b.
Answer: Resonance cross section ~ 1260 barns.

Chapter 10: Nuclear Reactions