Starting with N = N0e-λt, obtain a relation between disintegration constant ‘λ’ of a radioactive element and its half life (T), various terms have their usual meaning. - Zigya

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Starting with N = N₀e^-λt, obtain a relation between disintegration constant ‘λ’ of a radioactive element and its half life (T), various terms have their usual meaning.

Expression for half life: The radioactive decay equation is,

straight N space equals space straight N subscript straight o space straight e to the power of negative λt end exponent space space space space space space space... space left parenthesis 1 right parenthesis when space straight t space equals space straight T comma space straight N space equals space straight N subscript straight o over 2 therefore space straight N subscript straight o over 2 space equals space straight N subscript straight o space straight e to the power of negative λt end exponent space or space straight e to the power of negative λt end exponent space equals space 1 half space space space space space space space space... space left parenthesis 2 right parenthesis thin space Taking space log space of space both space sides comma minus λT space log subscript straight e space straight e space equals space log subscript straight e space 1 space minus space log subscript straight e 2 space λT space equals space log space straight e space 2 straight T space equals space fraction numerator log subscript straight e 2 over denominator straight lambda end fraction space space space space space space space space space space space space space space space... space left parenthesis 3 right parenthesis thin space space space space equals space fraction numerator 20.3026 space log subscript 10 squared over denominator straight lambda end fraction space space space equals space fraction numerator 2.3026 space straight x space 0.3010 over denominator straight lambda end fraction straight T space equals space fraction numerator 0.6931 over denominator straight lambda end fraction space space space space space space space space space space space space space space space space space... space left parenthesis 4 right parenthesis

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