The half - life of a radioactive isotope X is 50 yr. 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

200 yr

250 yr

100 yr

150 yr

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Solution

200 yr

We space know space that space fraction numerator straight N over denominator straight N subscript straight o space end fraction space equals space open parentheses 1 half close parentheses to the power of bevelled fraction numerator begin display style bevelled straight t over straight t subscript 1 end style over denominator 2 end fraction end exponent 1 over 16 space equals space open parentheses 1 half close parentheses to the power of bevelled straight t over 50 end exponent straight t equals space 4 space straight x space 50 straight t space equals space 200 space yr

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