Chapter 13 - Nuclei

Beginner

Topper

1. Nucleus - Composition & Size

Nucleus contains protons and neutrons called nucleons. Z protons, A total, N=A-Z neutrons.

Radius R=R0 A^1/3 R0=1.2 fm, density ~2.3e17 kg/m3 same for all, atom 1e-10 m nucleus 1e-15 m.

Z protons A nucleons N=A-Z | R=R0 A^1/3 R0=1.2 fm | Density ~2.3e17 kg/m3 constant

Visual Learning Method: Nucleus protons neutrons, radius formula, density teaspoon billions tons.

Daily Analogy: Nucleus heavy tiny marble mountain weight.

Nucleus - Composition & Size

Revision Points - Easy:

Z protons, A total, N=A-Z.
R=1.2 fm A^1/3, density same super dense.
Atom mostly empty.

2. Mass Defect & Binding Energy

Mass defect delta m = Zmp+Nmn-M. BE=delta m c^2, 1u=931.5 MeV. BE/A peak Fe-56 8.8 MeV most stable.

Mass defect delta m=Zmp+Nmn-M | BE=delta m c^2 1u=931.5 MeV | BE/A peak Fe-56 8.8 MeV

Visual Learning Method: Free heavier than bound, BE/A curve iron peak.

Daily Analogy: Missing mass is glue energy, iron strongest glue per brick.

Mass Defect & Binding Energy

Revision Points - Easy:

Nucleus lighter than parts.
BE=delta m c^2.
Fe-56 most stable.

3. Nuclear Forces

Strong short range ~1-2 fm, charge independent, saturated, repulsive core, meson exchange.

Super strong short ~1-2 fm charge independent saturated repulsive core meson pi

Visual Learning Method: Strong short spring, meson ball passing.

Daily Analogy: Super glue only when touching.

Nuclear Forces

Revision Points - Easy:

Strongest but short range.
Same for pp nn pn.
Only neighbours.

4. Radioactivity - Alpha Beta Gamma

Alpha He-4 heavy paper stopped, beta n->p e anti nu medium Al, gamma photon no Z A lead needed.

Alpha He-4 paper stopped | Beta n->p e anti nu Al stops | Gamma photon lead needed

Visual Learning Method: Alpha beta gamma penetration paper Al lead.

Daily Analogy: Heavy ball stops quickly, tennis further, X-ray through walls.

Radioactivity

Revision Points - Easy:

Alpha helium heavy low penetration.
Beta electron medium.
Gamma photon high penetration.

5. Decay Laws & Half-life

dN/dt=-lambda N, N=N0 e^-lambda t, Activity lambda N Bq, T1/2=0.693/lambda, tau=1/lambda=1.44 T1/2, after n half N0/2^n.

N=N0 e^-lambda t | Activity lambda N | T1/2=0.693/lambda | tau=1/lambda=1.44 T1/2

Visual Learning Method: Exponential decay half each half-life.

Daily Analogy: Popcorn popping half each half-life random.

Decay Laws & Half-life

Revision Points - Easy:

Decay exponential.
Half-life time for half decay.
Mean life 1.44 half-life.

6. Nuclear Reactions & Q-value

Conserve charge A energy momentum, Q=(Mreact-Mprod)c^2 positive releases KE.

Conserve charge A energy momentum | Q=(Mreact-Mprod)c^2 positive releases

Visual Learning Method: Alpha decay Q 4.27 MeV beta 0.78 MeV.

Daily Analogy: Q profit mass difference to energy.

Nuclear Reactions & Q-value

Revision Points - Easy:

Check charge and A balance.
Q positive releases energy.

7. Fission & Fusion

Fission U-235+n->Ba+Kr+3n+200 MeV chain reactor control rods moderator, fusion D+T->He+n+17.6 MeV sun high T millions, both to Fe peak.

Fission U-235+n Ba Kr 3n 200 MeV chain reactor control rods | Fusion D+T He n 17.6 MeV sun high T | Both to Fe peak

Visual Learning Method: Fission fragments chain, fusion sun high temp, BE/A curve both to peak.

Daily Analogy: Fission breaking pile releases, fusion squeezing magnets needs push.

Fission & Fusion

Revision Points - Easy:

Fission heavy splits by neutron 200 MeV chain.
Reactor controls chain rods moderator.
Fusion light joins high temp sun.

8. Applications & Final Revision

Medical I-131 thyroid Co-60 cancer Tc-99m scan, C-14 dating 5730 yr, power reactor, smoke detector Am-241, safety lead distance time.

Medical I-131 Co-60 Tc-99m | C-14 dating 5730 yr | Power reactor | Smoke Am-241 | Safety lead distance time

Visual Learning Method: Doctor tracer, carbon dating fossil, power plant, smoke detector.

Daily Analogy: Carbon dating hourglass full living, after death sand falls half each half-life.

Applications & Final Revision

Revision Points - Easy:

Radioisotopes treat scan.
C-14 age fossils.
Nuclear power electricity.
Smoke detector alpha.

Gold Reference Table

Concept	Formula	Daily Life Visual
Radius	R=R0 A^1/3 R0=1.2 fm	Tiny size grows slowly
Density	~2.3e17 kg/m3	Teaspoon billions tons
Mass defect	delta m=Zmp+Nmn-M	Missing mass glue
BE	BE=delta m c^2 1u=931.5 MeV	Holds nucleus
BE/A peak	Fe-56 8.8 MeV	Most stable
Alpha	He-4 paper stopped	Heavy ball
Beta	n->p e anti nu Al stops	Tennis ball
Gamma	Photon lead needed	X-ray through walls
Decay law	N=N0 e^-lambda t	Popcorn exponential
Half-life	T1/2=0.693/lambda	Half each half-life
Activity	A=lambda N Bq	Decays per sec
Q-value	Q=(Mreact-Mprod)c^2	Profit energy
Fission	U-235+n Ba Kr 3n 200 MeV chain	Reactor power
Fusion	D+T He n 17.6 MeV high T	Sun stars