The formulas concerning radioactivity.

1. Radioactive decay formula: N(t) = N0 * e^(-λt)
- N(t) = number of radioactive atoms remaining at time t
- N0 = initial number of radioactive atoms
- λ = decay constant
- t = time elapsed

2. Half-life formula: T1/2 = ln(2) / λ
- T1/2 = half-life of the radioactive substance
- ln(2) = natural logarithm of 2
- λ = decay constant

3. Activity formula: A = λ * N
- A = activity of the radioactive substance
- λ = decay constant
- N = number of radioactive atoms

4. Decay constant formula: λ = ln(2) / T1/2
- λ = decay constant
- ln(2) = natural logarithm of 2
- T1/2 = half-life of the radioactive substance

5. Effective dose formula: E = Σ (wT * D)
- E = effective dose
- wT = tissue weighting factor
- D = absorbed dose in the tissue

6. Absorbed dose formula: D = Σ (D * wR)
- D = absorbed dose
- wR = radiation weighting factor

7. Exposure formula: X = Σ (Φ * wR)
- X = exposure
- Φ = air kerma
- wR = radiation weighting factor

8. Equivalent dose formula: H = D * wR
- H = equivalent dose
- D = absorbed dose
- wR = radiation weighting factor

Radioactive Decay

- Half-life (t₁/₂): The time required for half of a radioactive sample to decay.
- t₁/₂ = (ln 2) / λ
- Decay Constant (λ): The probability of decay per unit time.
- λ = ln 2 / t₁/₂

Activity (A)

- Definition: The number of decays per unit time.
- Units: Becquerel (Bq) or Curie (Ci)
- Relationship to Half-life:
- A = λN
- Relationship to Time:
- A(t) = A₀ - (1/2)^(t / t₁/₂)

Radioactive Equilibrium

- Secular Equilibrium: When the parent nuclide has a much longer half-life than the daughter nuclide.
- Transient Equilibrium: When the parent and daughter nuclides have similar half-lives.
- Activity of parent = Activity of daughter
- λp - Np = λd - Nd

Energy of Radioactive Decay

- α decay:
- Q = (Mp + Mc - Ma)c²
- β decay:
- Q = (Mp - Mn + Me - Ma)c²
- γ decay:
- Q = 0 (since no mass is lost)

where:
- M is the mass in atomic mass units (amu)
- c is the speed of light
- p is the parent nuclide
- d is the daughter nuclide
- a is the α particle
- β is the β particle
- γ is the γ ray
- e is the electron