Home
Class 12
CHEMISTRY
A sample of uranium mineral was found to...

A sample of uranium mineral was found to contain `.^(206)Pb` and `^(238)U` in the ratio of `0.008 : 1` . Estimate the age of the mineral (half-life of `.^(238)U` is `4.51xx10^(9)` years).

Text Solution

Verified by Experts

`t=(2.303)/(lambda)log[1+(.^(206)Pb)/(.^(238)U)]`
`t=(2.303)/(0.693)xxt_(1//2)xxlog[1+(.^(206)Pb)/(.^(238)U)]`
`implies` Ratio by mass `.^(206)Pb : .^(238)U=0.008 : 1`
Ratio by moles `.^(206)Pb : .^(238)U=(0.008)/(206) : (1)/(238)`
`=0.0092`
`:. t=(2.303xx4.51xx10^(9))/(0.693)log(1+0.0092)` `=(2.303xx4.51xx10^(9))/(0.693)xx0.00397`
`=(0.0412)/(0.693)xx10^(9)=5.945xx10^(7)` years
Promotional Banner

Topper's Solved these Questions

  • CHEMICAL KINETICS AND RADIOACTIVITY

    FIITJEE|Exercise Example|5 Videos

  • CHEMICAL KINETICS AND RADIOACTIVITY

    FIITJEE|Exercise Solved problem (subjective)|15 Videos

  • CHEMICAL EQUILIBRIUM

    FIITJEE|Exercise MATCHING TYPE QUESTIONS|3 Videos

  • CHEMISTRY IN EVERY DAY LIFE

    FIITJEE|Exercise ASSIGNMENT PROBLEMS (OBJECTIVE) Level - II (Numerical Based Questions)|5 Videos

Similar Questions

Explore conceptually related problems

A sample of uranium mineral was found to contain Pb^(208) and U^(238) in the ratio of 0.008 : 1. Estimate the age of the mineral (half life of U^(238) is 4.51 xx 10^(9) years).

A uranium mineral contains .^(238)U and .^(206)Pb in the ratio of 4 : 1 by weigh. Calculate the age of the mineral, t_(1//2) .^(238)U = 4.5 xxx 10^(9) years. Assume that all the lead present in the mineral is formed from disintegration of .^(238)U .

In a smaple of rock, the ration .^(206)Pb to .^(238)U nulei is found to be 0.5. The age of the rock is (given half-life of U^(238) is 4.5 xx 10^(9) years).

(a) On analysis a sample of uranium ore was found to contian 0.277g of ._(82)Pb^(206) and 1.667g of ._(92)Pb^(206) and 1.667g of ._(92)U^(238) . The half life period of U^(238) is 4.51xx10^(9) year. IF all the lead were assumed to have come from decay of ._(92)U^(238) , What is the age of earth? (b) An ore of ._(92)U^(238) is found to contain ._(92)U^(238) and ._(82)Pb^(206) in the weight ratio of 1: 0.1 The half-life period of ._(92)U^(238) is 4.5xx10^(9) year. Caluculate the age of ore.

In a sample of pitchbende, the atomic ratio of .^(206)Pb : .^(238)U is 0.23 : 1. Calculate the age of the mineral if half life of uranium is 4.5 xx 10^(9) years. Assume that all lead has originated from uranium.

On analysis a sample of uranium are was found to contain 227g of ._(82)Pb^(208) and 1.667 g of ._(92)U^(238) . The half life peiod of U^(238) is 4.51 xx 10^(9) yrs. If all the lead was assumed to have come from decay of ._(92)U^(238) , what is the age of the earth?

._(92)U^(238) is radioactive and it emits alpha and beta particles to form ._(82)Pb^(206). Calculate the number of alpha and beta particles emitted in this conversion. An ore of ._(92)U^(238) is found ot contain ._(92)U^(238) and _(82)Pb^(206) in the weight ratio of 1: 0.1. The half- life -period of ._(92)U^(238) is 4.5xx 10^(9) yr. Calculate the age of the ore.