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

Barium-139 is the correct answer.

Answer 2

Barium-139

Step-by-step 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) = (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