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2)The isotope gold-198 is a β emitter and is used for the treatment of leukemia. The...

2)The isotope gold-198 is a β emitter and is used for the treatment of leukemia. The Half-life for its radioactive decay is 2.70 days. If the initial dose emits 60.0 mCi (mili Curies) of radiation, how many days will it take for the radiation level to drop to 7.50 mCi ?

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Answer #1

Given:
Half life = 2.7 days
use relation between rate constant and half life of 1st order reaction

k = (ln 2) / k
= 0.693/(half life)
= 0.693/(2.7)
= 0.2567 days-1

we have:
[A]o = 60 mCi
[A] = 7.5 mCi
k = 0.2567 days-1

use integrated rate law for 1st order reaction
ln[A] = ln[A]o - k*t
ln(7.5) = ln(60) - 0.2567*t
2.015 = 4.094 - 0.2567*t
0.2567*t = 2.079
t = 8.102 days
Answer: 8.10 days

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