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A radioactive material decays by simultaneous emission of two particles with half-lives 1620 yr and 810 yr respectively. The time in years after which one-fourth of material remains, is

1. 1080 yr
2. 2340 yr
3. 4860 yr
4. 3240 yr

Correct answer: 3240 yr

Solution

For simultaneous independent decays, the total decay constant is the sum of the individual constants. Using half-life relations, this gives an effective half-life of 1080 yr, so reaching one-fourth remaining takes two half-lives, i.e. 3240 yr.

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