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Chapter 04 · Part VI · Modern Physics
Revised on ____________________
Chapter 04 · Nuclei

Binding energy per nucleon decides everything

2 sheets
2 diagrams
24 results

Formulas and conditions only — no derivations, no solved numbers. The diagrams are the reader's own.

I

Size, mass and density

EVERY NUCLEUS HAS THE SAME DENSITY
I.Radius  R = R0 A1/3 R₀ = 1.2 fm
II.Volume  ∝ A so density is independent of A
III.Nuclear density  ≈ 2.3×1017 kg m−3
IV.Atomic mass unit  1 u = 931.5 MeV/c² = 1.66×10−27 kg
V.Mass defect  Δm = Z mp + N mn − M
VI.Isotopes / isobars / isotones  same Z / same A / same N
II

Binding energy

PER NUCLEON — NEVER THE TOTAL
I.Binding energy  Eb = Δm c²
II.Per nucleon  EbA the only measure of stability
III.Peak  8.79 MeV at 56Fe uranium: 7.59 MeV
IV.Light nuclei  fuse to climb the curve
V.Heavy nuclei  split to climb the curve
VI.Q value  Q = (Σmbefore − Σmafter) c² positive means it happens
both routes run uphill on this curvethat hill is where nuclear energy comes fromA246850100150200B/A (MeV)²H 1.1⁴Hethe iron peak · 8.8 MeV²³⁸Ufusionlight nuclei climbfissionheavy nuclei breakflat near 8 MeV across the table ⇒ B ∝ A: the nuclear force saturates
III

Radioactive decay

HALVING, NOT EMPTYING
I.Decay law  N = N0 e−λt
II.Activity  A = λ N = A0 e−λt becquerel; 1 Ci = 3.7×1010 Bq
III.Half-life  t½ = ln 2λ = 0.693λ after n of them, N0/2n — never zero
IV.Mean life  τ = 1λ = t½0.693 always longer than the half-life
V.α decay  (A, Z) → (A − 4, Z − 2) a helium nucleus
VI.β− decay  n → p + e− + ν γ decay changes neither A nor Z
each half-life halves what is leftthe same factor, measured from any moment you liket / t½NN₀11214181234N = N₀ e^(−λt)λ t½ = ln 2 = 0.693the count falls toward zero and never arrives
IV

Fission and fusion

BOTH CLIMB THE SAME CURVE
I.Fission of 235U  ≈ 200 MeV per event ≈ 0.9 MeV per nucleon
II.Chain reaction  needs k ≥ 1 and a critical mass
III.Moderator  slows neutrons to thermal energies heavy water, graphite
IV.Fusion  2H + 3H → 4He + n + 17.6 MeV
V.Why it is hard  the Coulomb barrier needs ≈ 107 K
VI.Per nucleon  fusion releases far more than fission
1 u
931.5 MeV
R0
1.2 fm
Peak B/A
8.79 MeV (56Fe)
Fission
≈ 200 MeV
D–T fusion
17.6 MeV
1 curie
3.7×1010 Bq
V

Where the marks go

FOUR ERRORS, EVERY YEAR
Where marks are lost in this chapter
1Ranking stability by total binding energy. Uranium's is larger than iron's; iron is the more stable per nucleon.
2Saying two half-lives empty the sample. A quarter remains, and it never reaches zero.
3Believing the β− electron was already inside. It is created in the decay n → p + e− + ν.
4Reading a long half-life as a strong source. A = λN, so a longer t½ means less activity.