The half life of a radioactive isotope 'X' is 20 years. It decays to another element 'Y' which is stable. The two elements 'X' and 'Y' were found to be in the ratio 1:7 in a sample of a given rock. The age of the rock is estimated to be:

  • Option 1)

    100 years

  • Option 2)

    40 years

  • Option 3)

    60 years

  • Option 4)

    80 years

 

Answers (1)

As discussed in @8783

t_{\frac{1}{2}} = 20t_{\frac{1}{2}} = 20 \: years \:(For \:X)

X\rightarrow Y

Let at any time number of nucleus of X is N.

Then number of nucleus is 7N.

\therefore Total number of nucleus = N0 = 8N

\therefore N = \frac{N_{0}}{8}

\because N = \frac{N_{0}}{2\frac{t}{t_{\frac{1}{2}}}} = \frac{N_{0}}{8}

\Rightarrow t =3t_{\frac{1}{2}}

t = 60 years 


Option 1)

100 years

This answer is incorrect

Option 2)

40 years

This answer is incorrect

Option 3)

60 years

This answer is correct

Option 4)

80 years

This answer is incorrect

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