The half life of a radioactive substance is 20 minutes. The approximate time interval (t₂ - t₁) between the time t₂ when 2/3 of it has decayed and time t₁ when 1/3 of it had decayed is

14 min

20 min

28 min

7 min

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Solution

20 min

2 over 3 straight N subscript 0 space equals space straight N subscript 0 straight e to the power of negative λt subscript 1 end exponent 1 third straight N subscript 0 space equals space straight N subscript 0 straight e to the power of negative λt subscript 2 end exponent 2 space equals straight e to the power of straight lambda left parenthesis space straight t subscript 2 minus straight t subscript 1 right parenthesis end exponent straight lambda left parenthesis straight t subscript 2 minus straight t subscript 1 right parenthesis space equals space l n 2 left parenthesis straight t subscript 2 minus straight t subscript 1 right parenthesis space equals space fraction numerator l straight n begin display style 2 end style over denominator straight lambda end fraction space equals space 20 space min

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