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

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.

Answer 2

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 =
`(t)/(t_(1/2))`

=
`(365)/(121)`

=
`3.01`

= 3.

Let the amount left after one year is N.

Hence, the rest amount of specimen is calculated as-

`(N)/(N_(0)) =\ ((1)/(2))^n`

`=\ ((1)/(2))^3`

`=\ (1)/(8)`

⇒
`N=\ N_(0)* (1)/(8)`

`=\ (24)/(8)\ Kg`

`=\ 3\ Kg` [ans][