Question

Tungsten, W-181, is a radioactive isotope with a half life of 121 days. If a medical lab purchases 24 kg of W-181, how much will be left after 1 year? A) 24 kg B) 12 kg C) 6 kg D) 3 kg

Answer 1

The correct answer of this question is : 3 Kg

EXPLANATION :

As per the question, the half life period of W-181 :  $t_{1/2}=\ 121\ days$

The initial amount of the specimen $N_{o}=\ 24\ Kg$

We are asked to calculate the amount of specimen left after one year.

Hence, the total time t = one year = 365 days.

Hence, total number of half lives n = $\frac{t}{t_{1/2}}$

                                                          = $\frac{365}{121}$

                                                          = $3.01$

                                                          = 3.

Let the amount left after one year is N.

Hence, the rest amount of specimen is calculated as-

                          $\frac{N}{N_{0}} =\ (\frac{1}{2})^n$

                                $=\ (\frac{1}{2})^3$

                                $=\ \frac{1}{8}$

                       ⇒ $N=\ N_{0}\times \frac{1}{8}$

                                $=\ \frac{24}{8}\ Kg$

                                $=\ 3\ Kg$                    [ans][

Answer 2

D) 3 kg
One year is approximately 3 half lives of W-181. The amount remaining would be 1/23 or 1/8. That is 3 kg of W-181.