The half-life of a radioactive isotope 'X' is 50 years. It decays to another element 'Y' which is stable. The two elements 'X' and 'Y' were found to be in the ratio of 1:15 in a sample of a given rock. The age of the rock was estimated to be

  • Option 1)

    150 years

  • Option 2)

    200 years

  • Option 3)

    250 years

  • Option 4)

    100 years

 

Answers (1)

As we learnt in 

Number of nuclei in terms of half life -

N=frac{N_{0}}{2^{t/t_{1/2}}}

- wherein

Very useful to determine number of nuclei in terms of half life

 

 At any time Ratio of X and Y is 1:15

if number of nuclei of X is N

then number of nuclei of Y is 15 N

Total number of nuclei initially and finally must be equal

\\ \Rightarrow N_{o}=16 N \\ \\ \Rightarrow N=\frac{N_{o}}{16} \: = \frac{N_{o}}{2^{\tfrac{t}{t_\frac{1}{2}}}} \: or \: \: \frac{t}{t_\frac{1}{2}}=4

t=4 \: t_\frac{1}{2} \: = \: 200 years


Option 1)

150 years

Incorrect

Option 2)

200 years

Correct

Option 3)

250 years

Incorrect

Option 4)

100 years

Incorrect

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