Vedatom Physics
Modern Physics / The Nucleus
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The quantum toolkit
1 u = 931.5 MeV/c²
r₀ = 1.2 fm
mₚ = 1.007276 u
mₙ = 1.008665 u
N_A = 6.022×10²³
1 fm = 10⁻¹⁵ m
1 Ci = 3.7×10¹⁰ Bq
ln2 = 0.693
Masses in u, energies in MeV, sizes in fm. Keep 1 u = 931.5 MeV and T½ = 0.693/λ close — they carry most of this chapter.
full reference ↗
Modern Physics · six modules lighting up one bench at a time
§01

How big is a nucleus — and how dense?

Scattering experiments give a strikingly simple rule: the radius grows as the cube root of the mass number, R = r₀A1/3 with r₀ ≈ 1.2 fm. Because volume ∝ R³ ∝ A, every nucleon takes up the same room — so nuclear density is essentially constant, about 2.3×10¹⁷ kg/m³, whether you weigh helium or uranium. Slide the mass number and watch the ball swell while the density needle never moves.

mass number AA = {{ szA }} · {{ szName }}
radius R
{{ szR }}
fm
R / R(proton)
{{ szRatio }}
= A1/3
density ρ
2.3
×10¹⁷ kg/m³ · fixed
R = r₀ A13· r₀ = 1.2 fm
ρ = massvolume = A·mN⁴⁄₃πR³→ A cancels
§05

Mass defect — where the binding energy hides

Add up the masses of the loose protons and neutrons, then weigh the assembled nucleus: it comes out lighter. That missing mass — the mass defect Δm = Zm_p + Nm_n − M — is exactly the energy that had to leave for the nucleus to bind: B = Δm·c² = Δm(u)×931.5 MeV. Pick a nuclide and watch the ledger; divide by A and you land back on the §03 curve.

Bench · loose nucleons → bound nucleus + energy
mass defect Δm
{{ mdefDm }}
u
binding B
{{ mdefB }}
MeV
B / A
{{ mdefPer }}
MeV/nucleon
{{ mdefZ }} m_p + {{ mdefN }} m_nΣm = {{ mdefSum }} u
− mass of {{ mdefName }}M = {{ mdefM }} u
= mass defect Δm{{ mdefDm }} u
B = Δm·c² = Δm(u) × 931.5 MeV
§03

Binding energy — the road to iron

Assembled nucleons weigh less than their loose parts — the missing mass Δm reappears as binding energy B = Δm·c². Divide by A and you get the single most important curve in nuclear physics. It climbs steeply, peaks near ⁵⁶Fe at about 8.8 MeV per nucleon, then eases down. Everything below the peak on the left releases energy by fusing; everything on the right releases energy by splitting. Slide the mass number and read which way energy wants to flow.

mass number AA = {{ baA }} · {{ baName }}
B / A
{{ baPerA }}
MeV / nucleon
total B ≈
{{ baTotal }}
MeV
{{ baRegimeTag }}
{{ baRegimeNote }}