Answer :
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.
The correct answer of this question is : 3 Kg
EXPLANATION :
As per the question, the half life period of W-181 : [tex]t_{1/2}=\ 121\ days[/tex]
The initial amount of the specimen [tex]N_{o}=\ 24\ Kg[/tex]
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 = [tex]\frac{t}{t_{1/2}}[/tex]
= [tex]\frac{365}{121}[/tex]
= [tex]3.01[/tex]
= 3.
Let the amount left after one year is N.
Hence, the rest amount of specimen is calculated as-
[tex]\frac{N}{N_{0}} =\ (\frac{1}{2})^n[/tex]
[tex]=\ (\frac{1}{2})^3[/tex]
[tex]=\ \frac{1}{8}[/tex]
⇒ [tex]N=\ N_{0}\times \frac{1}{8}[/tex]
[tex]=\ \frac{24}{8}\ Kg[/tex]
[tex]=\ 3\ Kg[/tex] [ans][
