Question

The half-life to a radioactive nucleus is 50 days. The time interval (t₂-t₁) between the time t₂ when 2/3 of it has decayed and the time t₁ when 1/3 of it had decayed is

30 days

50 days

60 days

15 days

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Solution

50 days

Active space fraction space straight a space straight t space instant space straight t subscript 2 1 over 2 to the power of straight t subscript 2 divided by straight T subscript 1 divided by 2 end subscript end exponent space equals space 1 third Active space fraction space straight a space straight t space instant space straight t subscript 1 1 over 2 to the power of straight t subscript 1 divided by straight T subscript 1 divided by 2 end subscript end exponent space equals space 2 over 3 2 to the power of straight t subscript 2 divided by straight T subscript 1 divided by 2 end subscript end exponent over 2 to the power of straight t subscript 1 divided by straight T subscript 1 divided by 2 end subscript end exponent space equals space 2 2 to the power of fraction numerator straight t subscript 2 divided by straight T subscript 1 divided by 2 end subscript over denominator straight t 1 divided by straight T subscript 1 divided by 2 end subscript end fraction end exponent space equals 2 straight t subscript 2 minus straight t subscript 1 space equals space straight T subscript 1 divided by 2 end subscript space equals space 50 space days

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