Rate of radioactive decay and half-life
Nuclear Chemistry · Chemistry
Study notes
A sample has 10⁶ radioactive nuclei with λ = 0.01 s⁻¹. Find activity now and nuclei left after 100 s. Step 1: A = λN = 0.01 × 10⁶ = 10⁴ decays/second (10 kBq). Step 2: N = N₀e^(-λt) = 10⁶·e^(-0.01×100) = 10⁶·e⁻¹. Step 3: e⁻¹ ≈ 0.368, so N ≈ 3.68×10⁵ nuclei remain. Step 4: t½ = 0.693/0.01 = 69.3 s — after ~69 s half are gone.