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Question Number 52457 by Necxx last updated on 07/Jan/19

Two radioactive elements A and B  has half lives of 100 and 50years.  Samples of A and B initial contains  equal numbers of atoms.What is  the ratio of the remaining atoms  of A to that of B after 200years?

$${Two}\:{radioactive}\:{elements}\:{A}\:{and}\:{B} \\ $$$${has}\:{half}\:{lives}\:{of}\:\mathrm{100}\:{and}\:\mathrm{50}{years}. \\ $$$${Samples}\:{of}\:{A}\:{and}\:{B}\:{initial}\:{contains} \\ $$$${equal}\:{numbers}\:{of}\:{atoms}.{What}\:{is} \\ $$$${the}\:{ratio}\:{of}\:{the}\:{remaining}\:{atoms} \\ $$$${of}\:{A}\:{to}\:{that}\:{of}\:{B}\:{after}\:\mathrm{200}{years}? \\ $$

Answered by MJS last updated on 07/Jan/19

t=000 A=100% B=100% A:B=1:1  t=100 A=50%  B=25% A:B=2:1  t=200 A=25% B=6.25% A:B=4:1

$${t}=\mathrm{000}\:{A}=\mathrm{100\%}\:{B}=\mathrm{100\%}\:{A}:{B}=\mathrm{1}:\mathrm{1} \\ $$$${t}=\mathrm{100}\:{A}=\mathrm{50\%}\:\:{B}=\mathrm{25\%}\:{A}:{B}=\mathrm{2}:\mathrm{1} \\ $$$${t}=\mathrm{200}\:{A}=\mathrm{25\%}\:{B}=\mathrm{6}.\mathrm{25\%}\:{A}:{B}=\mathrm{4}:\mathrm{1} \\ $$

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