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Fallout from nuclear explosions contains...

Fallout from nuclear explosions contains `""(131)I and ""^(90)Sr`. Calculate the time required for the activity of each of these isotopes to fall to `1.0%` of its initial value. Radioiodine and radiostrontium tend to concentrate in the thyroid and the bones, respectively, of mammals which ingest them. Which isotope is likely to produce the more serious long-term effects ? Half-life of `""^(131)I = 8` days, `""^(90)Sr = 19.9` yrs

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The correct Answer is:
`53.1` days, 132 yrs, `""^( 90)Sr` is likely to be serious, the iodine will soon be gone
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A radioactive nucleus A decays into B with a decay constnat lambda_(1) . B is alos radioactive and it decays into C with a decay constant of lambda_(2) . At time t=0 activity of A was recorded as A_(1)^(0) and that of B was A_(2)^(0)=0 , in a sample. (a) If N_(1) and N_(2) are population of nuclei of A and B respectively at time t, set up a differential equation in N_(2) . (b) The solution to the differential equation obtained in part(s) is given by (b) The solution to the differential equation obtained in part (a) is given by N_(2)=(lambda_(1))/(lambda_(2)-lambda_(1))N_(1)^(0)(e^(-lambda_(1)l)-e^(-lambda_(2)l)) Where N_(1)^(0) is initial population of A. Based on this answer following questions- (i) If half life of A is quite large compared to B (for example hafl life of A is 8 hr and that of B is 1hr). show that ratio of activity of B to that of A approaches a constant value after a sufficiently long time. Find this ratio, in terms of lambda_(1) and lambda_(2) . (ii) If half of A is inifinitely large compared to that of B (for example, A has half life -10^(9) yr and for B half life -10^(5) yr), show that both A and B will have equal activity after a very long time. (iii) If lambda_(1)gtlambda_(2) find the time at which activity of B reaches a maximum.

MOTION-RADIOACTIVITY -EXERCISE - 3
  1. Fallout from nuclear explosions contains ""(131)I and ""^(90)Sr. Calcu...

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  2. .(84)Po^(218) (t(1//2) = 3.05 min) decays to .(82)Pb^(214) (t(1//2) = ...

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  3. Potassium having atomic mass = 39.1 u contains 93.10 mass % ""^(39)K, ...

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  4. A mixture of ""^(239)Pu and ""^(240)Pu has a specific activity of 6 xx...

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  5. In a nature decay chain series starts with ""(90)Th^(232) and finally ...

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  6. A sample of {:(131),( 53):} I, as iodine ion, was administered to a pa...

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  7. A sample of Uraninite, a Uranium containing mineral was found on analy...

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  8. .(92)^(238)U by successive radioactive decays changes to .(82)^(206) P...

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  9. A sample pitch blende is found to contain 50% Uranium (U^(238)) and 2....

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  10. A 10 mL sample of a solution containing 1.0 xx 10^(–7) Ci of {:(3),(1...

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  11. Nuclei of a radioactive element A are being produced at a constant rat...

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  12. Nuclei of a radioactive element 'A' are being produced at a constant r...

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  13. Nuclei of a radioactive element 'A' are being produced at a constant r...

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  14. Mass defect in the nuclear reactions may by expressed in terms of the ...

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  15. Mass defect in the nuclear reactions may by expressed in terms of the ...

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  16. 1 Curie is equal to.

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  17. {:(14),(6):}C decays by emission of .

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  18. Emission of a beta - particle by a nuclide results in the formation o...

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  19. The number of alpha and beta - particles emitted, when the following...

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  20. The nuclides with same difference of number of neutrons and number of ...

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