A medical source has initial activity 8.00 MBq and half-life 6.00 h. Each detected decay deposits on average 0.500 MeV in 0.200 kg of tissue, and only 2.00% of all source decays deposit this energy there. Calculate activity after 18.0 h, total decays during the first 18.0 h, absorbed energy and dose. If shielding halves the depositing fraction, state its effect on activity and dose. Use 1 eV = 1.602 × 10⁻¹⁹ J.

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Activity after 18 h = 1.00 MBq; total decays = 2.18 × 10¹¹; deposited energy ≈ 0.349 J; dose ≈ 1.75 Gy. Shielding does not change source activity but halves tissue dose. Eighteen hours is three half-lives, so A = A₀/2³ = 1.00 MBq. Decay constant is λ = ln2/(6.00×3600) = 3.209 × 10⁻⁵ s⁻¹. Total decays are N_dec = (A₀/λ)(1−e^(−λt)) = (8.00 × 10⁶/λ)(1−1/8) = 2.18 × 10¹¹. Depositing decays are 0.0200N_dec. Energy per depositing decay is 0.500 × 10⁶(1.602 × 10⁻¹⁹) = 8.01 × 10⁻¹⁴ J. Deposited energy is approximately 0.349 J. Absorbed dose is energy per mass = 0.349/0.200 = 1.75 J kg⁻¹ = 1.75 Gy. External shielding changes the fraction of emitted radiation reaching tissue but not the nuclear decay probability inside the source. Halving the depositing fraction halves energy and absorbed dose while source activity follows the same half-life.

Activity, absorbed dose and shielding

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