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The mineral monazite is a rich source of...

The mineral monazite is a rich source of thorium, available in large quantity in kerala. A typical monazite sample contains 9% `ThO_(2)` and 0.35% `U_(3)O_(8)`. `.^(208)Pb` and `.^(206)Pb` are the stable end products in the radioactive decay series of `.^(232)Th` and `.^(238)U` respectively. All the lead in monazite is of radiogenic origin.
The isotopic ratio of `.^(208)Pb//^(232) Th`. was found to be 0.104. The half lives of Th and U are `1.41 xx 10^(10)` years adn `4.47 xx 10^(9)` years respectively.
The time elapsed since the formation of monazite sample will be:

A

`1.34 xx 10^(9)` years

B

`2.01 xx 10^(9)` years

C

`1.41 xx 10^(9)` years

D

`4.47 xx 10^(9)` years

Text Solution

Verified by Experts

The correct Answer is:
b
`(0.693)/(t_(1//2)Th) = (2.303)/(t_("age")) log ((N_(0))/(N))`
`(0.693)/(1.41 xx 10^(10)) = (2.303)/(t_("age")) log (1.104)`
`t_("age") = 2.01 xx 10^(9)` years
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Beach sand mineral, monazite, is a rich source of thorium, available in large quantities in the state of Kerala in india. A typical monazite sample contains about 9% ThO_(2) and 0.35% U_(3)O_(8). ^(208)Pb and ^(206)Pb are the stable end-products in the redioactive decay series of ^(232)Th and .^(238)U , respectively. All the lead (Pb) found in monazite is of radiogenic origin. The isotopic atom ratio ^(208)Pb//^(232)Th and .^(238)U are 1.41xx10^(10) years and 4.47xx10^(9) years, respectively. Assume that ^(208)Pb, ^(232)Th and .^(238)U remained entirely in the monazite sample since the formation of monazite mineral. Thorium- 232 is a fertile material for nuclear energy. In thermal neutron irradiation, it absorbs a neutron and the resulting isotope forms ^(233)U by successive beta -decays. Write the nuclear reactions for the formation of ^(233)U from ^(232)Th . In nuclear fission of ^(233)U a complex mixture of radioactive decay as shown below: _(42)^(101)Mo underset(t_(1//2)=14.6 min)(rarr) _(43)^(101)Tc underset(t_(1//2)=14.3 min)(rarr) _(44)^(101)Ru

Monazite sample contains 9% ThO""_(2) and 0.35% U""_(3)O""_(8).Pb""^(208) and Pb""^(206) are the stable and products in the radioactive decay series of Th""^(232) and U""^(238) respectively. All the lead in mozaite is of radiogenic origin. The isotopic ratio of Pb""^(208)/Th""^(232) was found to be 0.104. The half lives of Th and U are 1.41xx10""^(16) years and 4.47xx10""^(9) years respectively. Select the information incorrect about Th""^(232)

Knowledge Check

  • The mineral monazite is a rich source of thorium, available in large quantity in kerala. A typical monazite sample contains 9% ThO_(2) and 0.35% U_(3)O_(8) . .^(208)Pb and .^(206)Pb are the stable end products in the radioactive decay series of .^(232)Th and .^(238)U respectively. All the lead in monazite is of radiogenic origin. The isotopic ratio of .^(208)Pb//^(232) Th . was found to be 0.104. The half lives of Th and U are 1.41 xx 10^(10) years adn 4.47 xx 10^(9) years respectively. Estimated isotopic ratio of .^(206)Pb//^(238) U in the monazite sample will be:

    A
    0.166
    B
    0.266
    C
    0.366
    D
    0.466

  • Monazite sample contains 9\% ThO_(2) and 0.35\% U_(3)O_(8).Pb^(208) and Pb^(206) are the stable and products in the radioactive decay series of Th^(232) and U^(238) respectively. All the lead in mozaite is of radiogenic origin. The isotopic ratio of Pb^(208)/Th^(232) was found to be 0.104. The half lives of Th and U are 1.41xx10^(16) years and 4.47xx10^(9) years respectively. The time elpsed since the formation of monazite sample will be

    A
    `1.34xx10""^(9)years`
    B
    `2.01xx10""^(9)years`
    C
    `1.41xx10""^(9)years`
    D
    `4.47xx10""^(9)years`

  • Monazite sample contains 9% ThO""_(2) and 0.35% U""_(3)O""_(8).Pb""^(208) and Pb""^(206) are the stable and products in the radioactive decay series of Th""^(232) and U""^(238) respectively. All the lead in mozaite is of radiogenic origin. The isotopic ratio of Pb""^(208)/Th""^(232) was found to be 0.104. The half lives of Th and U are 1.41xx10""^(16) years and 4.47xx10""^(9) years respectively. Estimated isotopic ratio of Pb""^(206)//U""^(238) in the monazite sample will be

    A
    0.166
    B
    0.266
    C
    0.366
    D
    0.466

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