💡 Nuclear physics
Nuclear radius R = R₀ A^(1/3) (R₀ ≈ 1.2–1.4 fm). Mass defect Δm = Z m_p + (A−Z) m_n − M_nucleus. Binding energy BE = Δm × c² ≈ Δm × 931.5 MeV/u; BE/A maximum ~8.8 MeV/nucleon. Decay: λ = 0.693/T₁/₂, N = N₀ e^(-λt), activity A = λN. Q-value = (mass reactants − mass products) c² (positive = exoergic).
Nuclear physics calculators
Radius, mass defect, BE, decay, Q-value
Mass number (A)
A
R₀ (fm)
Nuclear radius
4.6 fm
Proton number (Z)
Z
Mass number (A)
A
Mass of nucleus (u)
u
Mass defect
0.528 u
Mass defect Δm (u)
u
Mass number (A, for BE/A)
A
Binding energy & per nucleon
492 MeV, 8.79 MeV/nucleon
Half-life (T₁/₂)
Initial number N₀ (optional)
nuclei
Elapsed time (t)
Decay constant, N remaining, Activity
—
Mass of reactants (u)
u
Mass of products (u)
u
Q-value
233 MeV (exoergic)
☢️ Nuclear summary
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🧮Step-by-Step Solution▼ Show
| Concept | Formula | Notes |
|---|---|---|
| Nuclear radius | R = R₀ A^(1/3) | R₀ ≈ 1.2–1.4 fm, A = mass number |
| Mass defect | Δm = Z m_p + (A−Z) m_n − M_nucleus | In u or kg |
| Binding energy | BE = Δm × c² = Δm × 931.5 MeV/u | Most stable around Fe-56 |
| BE per nucleon | BE / A | Maximum ~8.8 MeV/nucleon |
| Decay constant | λ = ln(2) / T₁/₂ = 0.693 / T₁/₂ | T₁/₂ = half-life |
| Nuclei remaining | N = N₀ e^(−λt) | Exponential decay |
| Activity | A = λ N = A₀ e^(−λt) | Bq or Ci |
| Q-value | Q = (m_reactants − m_products) c² | Positive → exoergic |
About nuclear physics
Nuclear radius follows R = R₀ A^(1/3) (A = mass number). Mass defect is the difference between the sum of nucleon masses and the actual nucleus mass; BE = Δm × c² ≈ Δm × 931.5 MeV/u. Binding energy per nucleon peaks near iron (Fe-56). Radioactive decay: λ = 0.693/T₁/₂, N = N₀ e^(-λt), A = λN. Q-value of a reaction is the mass difference (reactants − products) in energy units; Q > 0 means exoergic.