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Question

Two radioactive materials X subscript 1 end subscript and X subscript 2 end subscript have decay constants 10 lambda and lambda respectively. If initially they have the same number of nuclei, then the ratio of the number of nuclei of X subscript 1 end subscript to that of X subscript 2 end subscript will be 1/e after a time

  1. 1 divided by left parenthesis 10 lambda right parenthesis    
  2. 1 divided by left parenthesis 11 lambda right parenthesis    
  3. 11 divided by left parenthesis 10 lambda right parenthesis    
  4. 1 divided by left parenthesis 9 lambda right parenthesis    

The correct answer is: 1 divided by left parenthesis 9 lambda right parenthesis


    N subscript 1 end subscript equals N subscript 0 end subscript e to the power of negative 10 lambda t end exponentand N subscript 2 end subscript equals N subscript 0 end subscript e to the power of negative lambda t end exponent
    rightwards double arrow fraction numerator N subscript 1 end subscript over denominator N subscript 2 end subscript end fraction equals fraction numerator 1 over denominator e end fraction equals e to the power of negative 1 end exponent equals e to the power of left parenthesis negative 10 lambda plus lambda right parenthesis t end exponent equals e to the power of negative 9 lambda t end exponent rightwards double arrow t equals fraction numerator 1 over denominator 9 lambda end fraction.

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