Physics by Lamhi: Not Your Boring Physics

CLASS 12 · CHAPTER 13 · MODERN PHYSICS

QUICK REVISION

Nuclei

Every key result from this chapter, boxed and ready for a last look before the exam. No derivations here, just what to recall and when to use it — for the full explanation, see the detailed notes.

1. Nuclear Size & Density

Nuclear radius
R=R0A1/3,R0≈1.2 fmR = R_0A^{1/3}, \qquad R_0\approx1.2\text{ fm}

Nuclear density ≈ 2.3×10¹⁷ kg/m³ for every nucleus, independent of A.

2. Mass Defect & Binding Energy

Mass defect
Δm=[Zmp+(A−Z)mn]−Mnucleus\Delta m = [Zm_p+(A-Z)m_n] - M_{nucleus}
Binding energy
ΔEb=Δm c2\Delta E_b = \Delta m\,c^2

Binding energy per nucleon rises, peaks near A ≈ 56 (iron), then falls — both fission of heavy nuclei and fusion of light nuclei move toward this peak, releasing energy.

3. Radioactive Decay Law — the exam trap

Decay law
N=N0e−λt=N0(12)t/T1/2N = N_0e^{-\lambda t} = N_0\left(\dfrac{1}{2}\right)^{t/T_{1/2}}
Half-life & mean life
T1/2=ln⁡2λ,τ=1λ=T1/2ln⁡2≈1.44 T1/2T_{1/2} = \dfrac{\ln2}{\lambda}, \qquad \tau = \dfrac{1}{\lambda} = \dfrac{T_{1/2}}{\ln2} \approx 1.44\,T_{1/2}
  1. 100% → 50%: takes exactly one half-life, T½.
  2. 50% → 25%: takes the SAME T½ again, not faster, not slower.
  3. 25% → 12.5%: still exactly T½ — every halving takes identical time, regardless of how much is left.
  4. 12.5% → 6.25% → 3.125% → ...: continues forever, N never reaches exactly zero at any finite t.

λ, T½, and τ are fixed properties of the nuclide — they never depend on the current amount of sample or on elapsed time. See it live: half-life simulation →

4. Types of Radioactive Decay

  1. Alpha (α): emits ⁴₂He; A falls by 4, Z falls by 2.
  2. Beta (β⁻): n → p + e⁻ + antineutrino; A unchanged, Z rises by 1.
  3. Gamma (γ): photon only; A and Z both unchanged, just a drop to a lower energy state.

Full derivations and worked examples: detailed notes →