Questions

A radioisotope X with a half life 1.4 × ${10}^{9}$ years decays to Y which is stable. A sample of the rock from a cave was found to contain X and Y in the ratio 1: 7 . The age of the rock is

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a

1.96×109 years

b

3.92×109 years

c

8.4MeV

d

8.40×109 years

NEW

detailed solution

Correct option is C

Number of Nuclei at t = 0Number of Nuclei at time t As per questionN0-xx=177N0-7x=x or x=78N0∴ Remaining nuclei of isotope X=N0-x=N0-78N0=18N0=123N0So three half lives would have been passed∴ t=nT1/2=3×1.4×109 years =4.2×109 years Hence, the age of the rock is 4.2×109 years.

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The half life period of a radioactive element X is same as the mean life time of another radioactive element Y. Initially both of them have the same number of atoms. Then

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