A radioactive sample contains 2.5 × 10^16 atoms of a radioactive isotope with a half-life...

A radioactive sample contains 2.5 × 10^16 atoms of a radioactive isotope with a half-life of 3.2 hours. If the sample undergoes β-decay with a branching ratio of 0.75 for the decay mode, and the average energy released per decay is 2.1 MeV:

(a) Calculate the initial activity of the sample in Bq.

(b) Calculate the mass of the sample in grams, given that the molar mass of the isotope is 220 g/mol.

(c) If the sample is left to decay for 10 half-lives, calculate the remaining activity and the energy released during this time.

(d) Assuming the sample is in a 0.5 cm thick aluminum container, calculate the attenuation coefficient (μ) for the β-particles emitted, and estimate the fraction of the initial activity that will be absorbed by the container.?

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Asked by Amanda on 21st March, 2025