Question

What is the half life of an isotope that decays to 12.5% of its original activity in 67.8 h?

Answer 1

The half life of any substance is the time required for it to reach half its original amount.

Let us assume that at start of reaction 100% amount is present. and now only 12.5% remains.

i.e. 100 % ---> 50% ----> 25% ----> 12.5%

It means that to reach 12.5%, three time intervals = three half life are used.

Suppose, half life of isotope = 'x'

Then, three half life = 3x = 67.8h

Therefore 'x' = 22.6 h

half life is 22.6h.

To justify:

After 22.6h, 50 % of isotope remains

After another 22.6h (total 45.2h), 25 % of isotope remains

After another 22.6h (total 67.8h), 12.5 % of isotope remains.

Hence proved

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