A given number of atoms, N0 of a radioactive element with a half life

2 answer

A given number of atoms, N0 of a radioactive element with a half life T is uniformly distributed in the blood stream of a
(i) normal person A having total volume V .of blood in the body
(ii) person B in need of blood transfusion having a volume V’ of blood in the body.
The number of radioactive atoms per unit volume in the blood streams of the two persons after a time { n }_{ 1 }
are found to be
{ N }_{ 2 }
and
{ N }_{ 2 }.
Prove mathematically that the additional volume of blood that needs to be transfused in the body of
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Initial number of radioactive atoms, per unit volume, in the blood streams of persons A and B are
11a29ae9b7317747ed52dfe6d3b699b7c1e474da.pngAfter a time nT (T = Half-life), these numbers would get reduced by a factor 2".
d1a7a9479e98897cf109f228e04e17acb31a0b58.png
Additional volume of blood needed by person B is
6e9b0a08388e7c8994ae6dac1bcfd218ed444d85.png