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PHYS 420: Astrophysics & Cosmology
Homework 02
Due in class: Thursday, Feb 9
1. Nuclear Binding Energy. A useful quantity when speaking of masses of
nuclei is the mass defect or mass excess. Defined through the
following: Mactual = AMamu + D, Where Mamu is the Atomic Mass Unit,
defined w.r.t. 12C, such that Mactual(12C) = 12Mamu. The Mass excess of
12
C is identically 0. In standard units Mamu=1.66053904x1027 kg =
931.494095 MeV/c2. A is the total number of nucleons (or baryons i.e.
neutrons & protons) in the nucleus.
a. Find an expression for the binding energy Bi of nuclide i in terms
of its mass defect ∆i (and possibly ∆p and/or ∆n). Also find an
expression for the reaction energy release or Q-value of a nuclear
reaction A(b, c)D in terms of the mass defects of the particles. In
other words, how much mass-energy is extra after converting A+b
into c+D?
b. On the web (e.g., the Nuclear Wallet Card webpage) you will find
a veritable panoply of nuclear data, including mass defect
information. Use this to compute the binding energy, and B/A, of
deuterium d, 4He, 12C, and 56Fe, and 238U. Find the Q value for
3
He(α, γ)7Be.
2. Conservation Laws. Consider the following processes. For each
reaction, state whether the reaction is allowed or forbidden, according to
the conservation laws we have discussed. If the reaction is forbidden,
indicate which law(s) are violated. If the reaction is allowed, indicate if it
is endothermic or exothermic. (Refer to the Particle Data Group
webpage for particle masses; you may take mν = 0.)
a. p + γ → p + π0
b. 𝜈 τ + τ− → µ− + 𝜈 µ
c. π− + p → n + π0
d. π+ + n → p