Radioactive Activity

Radioactive Activity

Activity $A$ is the number of decays per second. It is directly proportional to the number of radioactive nuclei $N$ present:

$A = \lambda N \quad [\text{Becquerel, Bq}]$

One Becquerel equals one decay per second. The older unit, the Curie (Ci), was defined as the activity of 1 gram of radium-226:

$1 \text{ Ci} = 3.7 \times 10^{10} \text{ Bq}$

Specific Activity

The specific activity is the activity per unit mass. For a pure isotope:

$A_{\text{spec}} = \frac{\lambda N_A}{M} = \frac{\ln 2}{t_{1/2}} \cdot \frac{N_A}{M} \quad [\text{Bq/kg}]$

where $N_A = 6.022 \times 10^{23}$ mol⁻¹ is Avogadro's number and $M$ is the molar mass in kg/mol.

Examples

• C-14 ($t_{1/2} = 5730$ yr, $M = 14 \times 10^{-3}$ kg/mol): high specific activity due to short half-life
• Ra-226 ($t_{1/2} = 1600$ yr, $M = 226 \times 10^{-3}$ kg/mol): ~1 Ci/g by definition
• U-238 ($t_{1/2} = 4.468 \times 10^9$ yr): very low specific activity

Your Task

Implement:

• activity_bq(N, lambda_s) — activity in Bq given number of nuclei and decay constant in s⁻¹
• bq_to_curie(activity_bq) — convert Bq to Curie
• specific_activity(half_life_s, molar_mass_kg_per_mol) — specific activity in Bq/kg

All constants ($N_A$, Ci definition) must be inside each function.