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A radioactive material of half-life T was produced in a nuclear reactor at different instants, the quantity produced second time was twice of that produced first time. If now their present activities are A subscript 1 space a n d space A subscript 2 respectively then their age difference equals:
(A) fraction numerator T over denominator ln 2 end fraction open vertical bar ln A subscript 1 over A subscript 2 close vertical bar
(B) T open vertical bar ln A subscript 1 over A subscript 2 close vertical bar
(C)fraction numerator T over denominator ln 2 end fraction open vertical bar ln fraction numerator A subscript 2 over denominator 2 A subscript 1 end fraction close vertical bar
(D) T open vertical bar l n fraction numerator A subscript 2 over denominator 2 A subscript 1 end fraction close vertical bar
Asked by yugibo | 13 Apr, 2016, 09:48: PM
answered-by-expert Expert Answer
begin mathsize 12px style Given space that space the space quantity space produced space second space time space was space twice space of space that space produced space first space time. We space know space that space straight A subscript 1 equals λN subscript straight o straight e to the power of negative λt subscript 1 end exponent or space straight t subscript 1 equals 1 over straight lambda space ln space open parentheses λN subscript straight o over straight A subscript 1 close parentheses and space space straight t subscript 2 equals 1 over straight lambda space ln space open parentheses fraction numerator straight lambda 2 straight N subscript straight o over denominator straight A subscript 2 end fraction close parentheses Age space diffrence space equals space straight t subscript 2 minus straight t subscript 1 space equals space 1 over straight lambda space ln space open parentheses fraction numerator straight A subscript 2 over denominator 2 straight A subscript 1 end fraction close parentheses But space straight T space equals space fraction numerator ln space 2 over denominator straight lambda end fraction therefore Age space d i f f e r e n c e space equals space straight t subscript 2 minus straight t subscript 1 space equals fraction numerator straight T over denominator ln space 2 end fraction ln space open vertical bar fraction numerator straight A subscript 2 over denominator 2 straight A subscript 1 end fraction close vertical bar end style
Answered by Yashvanti Jain | 15 Apr, 2016, 12:23: PM

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