Nuclear Physics (Copy)

A2 Level Physics – Section 23: Nuclear Physics (Detailed Notes)

23.1 Mass Defect and Nuclear Binding Energy

1. Mass-Energy Equivalence

• Energy and mass are interchangeable:
  E = mc²
  • E = energy (J)
  • m = mass (kg)
  • c = speed of light = 3.00 × 10⁸ m/s
• 1 unified atomic mass unit (u) = 1.66 × 10⁻²⁷ kg
  • Equivalent to 931.5 MeV

2. Nuclear Reactions

• Nuclear reactions are written using nuclear symbols:
  ₁₁H + ⁴₂He → ¹⁵₈O + ¹₀n
• Mass number and proton number are conserved.

3. Mass Defect and Binding Energy

• Mass defect (Δm):
  Difference between total mass of individual nucleons and the actual mass of the nucleus.
• Binding energy (BE):
  Energy required to separate all nucleons in a nucleus.
  BE = Δm·c²
• Binding energy per nucleon = BE / A
  (A = number of nucleons)

4. Binding Energy per Nucleon vs Nucleon Number

• Plot has a peak at iron (A ≈ 56) → most stable nuclei
• Light nuclei (A < 56): fusion increases BE/nucleon
• Heavy nuclei (A > 56): fission increases BE/nucleon

5. Nuclear Fusion and Fission

• Fusion: Small nuclei combine to form larger one
  • Occurs in stars (e.g. H + H → He)
  • Releases energy because product has higher BE/nucleon
• Fission: Large nucleus splits into smaller ones
  • Used in nuclear reactors (e.g. U-235)
  • Releases energy for the same reason

6. Relevance of Binding Energy per Nucleon

• Energy released in fusion/fission comes from increase in binding energy per nucleon
• Total binding energy increases → mass decreases → energy released

7. Calculating Energy Released

• From mass defect:
  E = Δm·c²
  • Δm in kg → E in joules
  • Or Δm in u → multiply by 931.5 to get energy in MeV

23.2 Radioactive Decay

1. Randomness of Decay

• Count rate fluctuates over time → evidence that decay is random
• Cannot predict which nucleus will decay, only probability

2. Spontaneous and Random

• Spontaneous: not influenced by external factors (e.g. pressure, temperature)
• Random: unpredictable for individual nuclei

3. Activity and Decay Constant

• Activity (A): rate of decay = number of disintegrations per second (unit: Bq)
• Decay constant (λ): probability of decay per unit time (s⁻¹)
• A = λ·N
  • N = number of undecayed nuclei

4. Half-Life (t½)

• Time for half of the nuclei to decay

λ = 0.693 / t½

5. Exponential Decay

• x = x₀·e^(–λt)
  • x = activity (A), count rate, or number of nuclei (N)
  • x₀ = initial value
  • λ = decay constant
  • t = time

Graph:

• Exponential curve falling toward zero
• Halves every t½