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Question

The half life of radioactive Radon is 3.8 days. The time at the end of which 1 divided by 2 0 to the power of t h end exponentof the Radon sample will remain undecayed is (Givenlog subscript 10 end subscript invisible function application e equals 0.4343)

  1. 3.8 days    
  2. 16.5 days    
  3. 33 days    
  4. 76 days    

The correct answer is: 16.5 days


    By the formula N equals N subscript 0 end subscript e to the power of negative lambda t end exponent
    Given fraction numerator N over denominator N subscript 0 end subscript end fraction equals fraction numerator 1 over denominator 20 end fractionand lambda equals fraction numerator 0.6931 over denominator 3.8 end fraction Þ 20 equals e to the power of fraction numerator 0.6931 cross times t over denominator 3.8 end fraction end exponent
    Taking log of both sides
    or log 20 equals fraction numerator 0.6931 cross times t over denominator 3.8 end fraction log subscript 10 end subscript invisible function application e
    or 1.3010equals fraction numerator 0.6931 cross times t cross times 0.4343 over denominator 3.8 end fraction Þ t equals 16.5days

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