1.1Use the Relativistic Energy Relation
What is the total energy of a particle at rest?
Solution
Set $p=0$ in $E^2=p^2c^2+m^2c^4$. The positive-energy solution is $E=mc^2$.
Particle and Nuclear Physics Practice
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Direct Practice
1.2Check a Reaction Charge
Can a reaction with total initial charge $+1e$ produce final particles with total charge $0$?
Solution
No. Electric charge is conserved, so the final total must also be $+1e$.
1.3Interpret a Half-Life
What fraction of a radioactive sample remains after three half-lives?
Solution
Each half-life halves the amount, so the remaining fraction is $(1/2)^3=1/8$.
1.4Compute Nuclear Binding Energy
A nucleus has constituent mass total $10.000\ \text{u}$ and measured nuclear mass $9.950\ \text{u}$. Estimate its binding energy using $1\ \text{u}\,c^2=931.5\ \text{MeV}$.
Solution
The mass defect is $\Delta m=0.050\ \text{u}$, so
$$
B=\Delta m c^2=(0.050)(931.5)\ \text{MeV}\approx46.6\ \text{MeV}.
$$
1.5Check Beta-minus Bookkeeping
Complete the beta-minus decay of a neutron: $n\rightarrow p+\ ?$.
Solution
The products are $p+e^-+\bar\nu_e$. Charge is conserved because the electron contributes $-1$ while the proton contributes $+1$, and lepton number is conserved by the electron antineutrino.