Question

The half life time period of radioactive substance is 30 days. What is the time taken for 3/4th of the original mass to disintegrate?

Answer 1

Solution :

The half life time period of a radioactive substance is 30 days .

We have to find the time taken for ¾ th of the original mass to disintegrate .

N(t) = N_0. (½)^(t/t_½)

N(t)/N_0 = (½)^(t/t_½)

Here, ¾th of the mass is disintegrating

N(t) = N_0 - ¾ N_0 = (1-¾) N_0 = ¼ N_0

Substituting this

¼N_0/(N_0) = (½)^(t/30). [ t_½ is 30 days as mentioned above]

So

¼ = ½^(t/30)

(½)² = (½)^(t/30)

t/30 = 2

t = 60 days.

Answer : The time taken for ¾th of the original mass to disintegrate is 60 days.

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