Half life of a radioactive element is 12.5 hour and its quantity is 256 g. After how much time its quantity will remain 1 g?

Question

Half life of a radioactive element is 12.5 hour and its quantity is 256 g. After how much time its quantity will remain 1 g? (A) 50 hrs (B) 100 hrs (C) 150 hrs (D) 200 hrs

Tardigrade Admin · Accepted Answer

(N/N0)=((1/2))n n arrow no. of decays. (1/256)=((1/2))8=((1/2))n ∴ n=8 Time for 8 half life =100 hours.

Q. Half life of a radioactive element is $12.5$ hour and its quantity is $256 g$ . After how much time its quantity will remain 1 g?

50 hrs

100 hrs

150 hrs

200 hrs

$\frac{N}{N _{0}} = (\frac{1}{2})^{n} n \to$ no. of decays.
$\frac{1}{256} = (\frac{1}{2})^{8} = (\frac{1}{2})^{n}$
$∴ n = 8$
Time for $8$ half life $= 100$ hours.

Q. Half life of a radioactive element is 12.5 hour and its quantity is 256g. After how much time its quantity will remain 1 g?