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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.

Knowledge Check

  • The process in which solution containing more than one typeof ions (either cation or anion) and in which one ion undergoes almst complete precipitation followed by the second ion and similarly second ion undergoes complete precipitation followed by the third ion is known as preferential precipitation. It is the solubility of the salt,not the solubility product of the salt, by means of which one can predict the preferential precipitation of the salt or ion among the lot of ions in the solution. For example , in a solution containing Cl^(-), Br^(-) and I^(-) ions, if Ag^(+) ions are added, then out of three , the less soluble salt is precipitated first . If the addition of Ag^(+) ions is continued, eventually , a stage is reached when the next lesser soluble salt starts precipitating along with the least soluble salt and so on. If the stiochiometry of the salt is same, then the salt with the minimum K_(sp) ( solubility product ) will have minimum solubility and will precipitate first, followed by the salt of next higher solubility product and so on. If the stiochiometry of teh salt is not same, then from the solubility product data alone, we cannot predict which ions will precipitate first. For example, a solution containing Cl^(-) and CrO_(4)^(2-) . In order to predict which ion will precipitate first, we have to calculate the amount of Ag^(+) ions needed to start precipitation through the solubility product data given. When AgNO_93) is added to the solution, the minimum of the two concentrations needed to start the precipitation will be reached and thus corresponding [Ag^(+)] to start the precipitation increases. Its concentration eventually becomes equal to the value required for CrO_(4)^(2-) . At this stage, practically almost the whole of Cl^(-) ions get precipitated . Addition of more AgNO_(3) causes simultaneous precipitation of both the ions together. Suppose a student of chemistry performs the following two sets of experiments in order to known the preferential precipitation of ions as well as its precipitated percentage amount. Experiment 1. He prepare a solution of anions composed of 0.1 M each of Cl^(-),Br^(-) and I^(-) . Further he adds gradually solid AgNO_(3) to this solution. He assumes that volume of the solution does not change after the addition of solid AgNO_(3)(K_(sp)AgCl=1.0 xx 10^(-9)M^(2),K_(sp) AgBr=10^(-10)M^(2) and K_(sp) AgI=10^(-12)M^(2)) Experiment -2. He prepares a solution of cations Cd^(2+)(0.2 M) and Bi^(3+) (0.3 m) . Now he adds S^(2-) ions into the solution of cations in order to separate them by selective precipitation Cd^(2+) forms yellow precipitate of CdS and Bi^(3+) forms black precipitate of Bi_(2)S_(3) with S^(2-) ions respectively. (K_(sp)Bi_(2)S_(3) = 9 xx 10^(-25) M^(5) and K_(sp)CdS =2 xx 10^(-20)M^(2)) .Answer the following questions ont he basis of the above write up. Which of the following will precipitate first in experiment -1 ?

    A
    `I^(-)`ion
    B
    `Br^(-)` ion
    C
    `Cl^(-)` ion
    D
    cannot be predicted

  • The process in which solution containing more than one typeof ions (either cation or anion) and in which one ion undergoes almst complete precipitation followed by the second ion and similarly second ion undergoes complete precipitation followed by the third ion is known as preferential precipitation. It is the solubility of the salt,not the solubility product of the salt, by means of which one can predict the preferential precipitation of the salt or ion among the lot of ions in the solution. For example , in a solution containing Cl^(-), Br^(-) and I^(-) ions, if Ag^(+) ions are added, then out of three , the less soluble salt is precipitated first . If the addition of Ag^(+) ions is continued, eventually , a stage is reached when the next lesser soluble salt starts precipitating along with the least soluble salt and so on. If the stiochiometry of the salt is same, then the salt with the minimum K_(sp) ( solubility product ) will have minimum solubility and will precipitate first, followed by the salt of next higher solubility product and so on. If the stiochiometry of teh salt is not same, then from the solubility product data alone, we cannot predict which ions will precipitate first. For example, a solution containing Cl^(-) and CrO_(4)^(2-) . In order to predict which ion will precipitate first, we have to calculate the amount of Ag^(+) ions needed to start precipitation through the solubility product data given. When AgNO_93) is added to the solution, the minimum of the two concentrations needed to start the precipitation will be reached and thus corresponding [Ag^(+)] to start the precipitation increases. Its concentration eventually becomes equal to the value required for CrO_(4)^(2-) . At this stage, practically almost the whole of Cl^(-) ions get precipitated . Addition of more AgNO_(3) causes simultaneous precipitation of both the ions together. Suppose a student of chemistry performs the following two sets of experiments in order to known the preferential precipitation of ions as well as its precipitated percentage amount. Experiment 1. He prepare a solution of anions composed of 0.1 M each of Cl^(-),Br^(-) and I^(-) . Further he adds gradually solid AgNO_(3) to this solution. He assumes that volume of the solution does not change after the addition of solid AgNO_(3)(K_(sp)AgCl=1.0 xx 10^(-9)M^(2),K_(sp) AgBr=10^(-10)M^(2) and K_(sp) AgI=10^(-12)M^(2)) Experiment -2. He prepares a solution of cations Cd^(2+)(0.2 M) and Bi^(3+) (0.3 m) . Now he adds S^(2-) ions into the solution of cations in order to separate them by selective precipitation Cd^(2+) forms yellow precipitate of CdS and Bi^(3+) forms black precipitate of Bi_(2)S_(3) with S^(2-) ions respectively. (K_(sp)Bi_(2)S_(3) = 9 xx 10^(-25) M^(5) and K_(sp)CdS =2 xx 10^(-20)M^(2)) .Answer the following questions ont he basis of the above write up. Which of the following is the correct order of appearance of coloour of the precipitate in experiment ?

    A
    yellow `gt` pale yellow `gt` curdy white
    B
    yellow `lt` pale yellow `lt` curdy white
    C
    pale yellow `gt` yellow `lt` curdy white
    D
    pale yellow `gt` yellow `gt` curdy white

  • The process in which solution containing more than one typeof ions (either cation or anion) and in which one ion undergoes almst complete precipitation followed by the second ion and similarly second ion undergoes complete precipitation followed by the third ion is known as preferential precipitation. It is the solubility of the salt,not the solubility product of the salt, by means of which one can predict the preferential precipitation of the salt or ion among the lot of ions in the solution. For example , in a solution containing Cl^(-), Br^(-) and I^(-) ions, if Ag^(+) ions are added, then out of three , the less soluble salt is precipitated first . If the addition of Ag^(+) ions is continued, eventually , a stage is reached when the next lesser soluble salt starts precipitating along with the least soluble salt and so on. If the stiochiometry of the salt is same, then the salt with the minimum K_(sp) ( solubility product ) will have minimum solubility and will precipitate first, followed by the salt of next higher solubility product and so on. If the stiochiometry of teh salt is not same, then from the solubility product data alone, we cannot predict which ions will precipitate first. For example, a solution containing Cl^(-) and CrO_(4)^(2-) . In order to predict which ion will precipitate first, we have to calculate the amount of Ag^(+) ions needed to start precipitation through the solubility product data given. When AgNO_93) is added to the solution, the minimum of the two concentrations needed to start the precipitation will be reached and thus corresponding [Ag^(+)] to start the precipitation increases. Its concentration eventually becomes equal to the value required for CrO_(4)^(2-) . At this stage, practically almost the whole of Cl^(-) ions get precipitated . Addition of more AgNO_(3) causes simultaneous precipitation of both the ions together. Suppose a student of chemistry performs the following two sets of experiments in order to known the preferential precipitation of ions as well as its precipitated percentage amount. Experiment 1. He prepare a solution of anions composed of 0.1 M each of Cl^(-),Br^(-) and I^(-) . Further he adds gradually solid AgNO_(3) to this solution. He assumes that volume of the solution does not change after the addition of solid AgNO_(3)(K_(sp)AgCl=1.0 xx 10^(-9)M^(2),K_(sp) AgBr=10^(-10)M^(2) and K_(sp) AgI=10^(-12)M^(2)) Experiment -2. He prepares a solution of cations Cd^(2+)(0.2 M) and Bi^(3+) (0.3 m) . Now he adds S^(2-) ions into the solution of cations in order to separate them by selective precipitation Cd^(2+) forms yellow precipitate of CdS and Bi^(3+) forms black precipitate of Bi_(2)S_(3) with S^(2-) ions respectively. (K_(sp)Bi_(2)S_(3) = 9 xx 10^(-25) M^(5) and K_(sp)CdS =2 xx 10^(-20)M^(2)) .Answer the following questions ont he basis of the above write up. What % of the (ion) will get precipitate when the second ion start precipitating in experiment -1 ?

    A
    `10%`
    B
    `90%`
    C
    `1%`
    D
    `99%`
    • 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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