Question

suppose that a radioactive isotope starts off with a certain amount of the radioactive element, which then decays. after 45 hours, the material has decayed to half of its original amount. how many hours would you have to wait for the isotope to decay from 100% to 12.5% of its original amount of the isotope?

Answer 1

After 135 hours the concentration of the isotope will decay to 12.5% of the initial concentration of the sample.

So, it is given that the half life of the sample which is radioactive is 45 ours.

It means, the concentration of the sample becomes half in every 45 hours.

So, let us say that the initial concentration of the sample is A.

So, after 45 hours the concentration will become A/2 which is 50% of A.

Now, the If initial concentration is taken as A/2 then after 45 more hours the concentration will be A/4 which is 25% of A.

Now, if the concentration is taken to be A/4, then again after 45 hours, the concentration will become A/8 which is 12.5% of A.

SO, it took (45 + 45 + 45) Hours.

It took 135 hours for concentration to decay to 12.5%.

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