Question

If the activity of a radioactive
sample drops to 1/16th
of its initial value in 3 hours,
It's half life is

Answer 1

Answer:

45 mins

Explanation:

Let the half life of the redioactive material = X mins

Thus, in X mins, the sample weight will be = 1/2 X

in next X mins, i.e., in 2X mins total, the weigh will reduce to half of the weight in x mins.

i.e. = (1/2) * [1/2 X] = 1/4X

i.e. = (1/2^2) X

∴ For every multiple of X... nX time, the weight of the sample will be 1/(2^n)

similarly, for weight of sample to drop to 1/16th of its initial value, the time taken will be..

1/16th = 1/ (2^4)

time taken will be 4X

but time give as 3 hrs = 180 min

∴ 4X = 180 min

∴ X = 45 min

Half life of the sample = 45 mins

Answer 2

Answer:

Half life of a radioactive substance is the time taken by it to reduce to half of it's amount. If the sample of radioactive substance drops to 1/16 of it's original amount. It means in the first half life, it reduces to 1/2, and then in the next half life it goes down to 1/4. The same way 4 half lives, amount reduces to 1/16.

This means 4 half lives = 3 hours(According to question)

So, it's half life = 3/4 hours

=3/4*60

=15 Minutes