Question

Rachel has an unknown sample of a radioisotope listed in the table. Using a special technique, she is able to measure the mass of just the unknown isotope as 104.8 kg at 12:02:00 P.M. At 4:11:00 P.M. on the same day, the mass of the unknown radioisotope is 13.1 kg. Which radioisotope is in the sample?

Answer 1

Answer:

Barium-139

Explanation:

initial mass of the sample at 12:02:00 PM is given as

$m_1 = 104.8 kg$

Mass of the sample at 4:11:00 PM is given as

$m_2 = 13.1 kg$

so here since it is a sample of radioactive isotope so here we will say

$m_2 = m_1 e^{-\lambda t}$

now from above data we know that the time taken to reduce the mass is

$t = 4 hours 9 minutes$

$t = 4.15 hours$

now from above equation we will have

$13.1 = 104.8 e^{-\lambda(4.15)}$

$\lambda(4.15) = 2.08$

$\lambda = 0.50 per hour$

so here half life is given as

$T_{1/2} = \frac{ln2}{\lambda}$

$T_{1/2} = 1.4 hours$

So here this isotope must be the one which will have half life of 1.4 hours

So it is nearly Barium-139

Answer 2

Barium-139 is the correct answer.