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Barium-131 is a radioactive isotope of the element barium used for gastrointestinal tract scans in doctors offices. Barium-131 has a half-life of 10 days. If a patient drinks 2 grams of barium-131 how much of the isotope will be left after 10 days?

A0.125 grams B) 0.25 grams C) 0.5 grams D) 1 gram

Verified Answer :

After 10 days 1 gram is left.

Answer:The correct answer is option D.

Explanation:

Amount of dose given to patient = \(N_o=2g\)

Half life of Barium-131 =\(t_{\frac{1}{2}}=10 days\)

Amount of barium-131 left after 10 days.

t = 10 days

\(\lambda =\frac{0.693}{t_{\frac{1}{2}}}=\frac{0.693}{10 days}= 0.0693 day^{-1}\)

\(N=N_o\times e^{-\lambda t}\)

\(\log N=\log N_o -\frac{\lambda t}{2.303}\)

\(\log N=\log [2]-\frac{0.0693 day^{-1}\times 10 days}{2.303}\)

\(N=0.999 g\approx 1 g\)

Hence, correct answer is option D.

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