Question

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?
A) 0.125 grams B) 0.25 grams C) 0.5 grams D) 1 gram

Answer 1

After 10 days 1 gram is left.

Answer 2

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.