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Question

Samples of two radioactive nuclides, X and Y, each have equal activity A at time t=0. X has a half-life of 24 years and Y a half-life of 16 years. The samples are mixed together. What will be the total activity of the mixture at t=48 years?

A
12A0
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B
14A0
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C
316A0
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D
38A0
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Solution

The correct option is D 38A0
If initial activity is A0
After 'n' half lifes, activity would reduce to A02n because number of nuclei would reduce by that much.
In 48 hours, substance X would undergo two half lives.
Its new activity would become A04
Substance Y would undergo three half lives.
Its new activity would become A08
The total activity would be the sum:
A04+A08=3A08

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