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The half-life of a radioactive isotope X is 20 yr. 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

Asked in NEET 2013 · Decay law and half-life

Answer: (2) 60 yr

Step-by-step solution

Each decayed nucleus of X becomes one nucleus of Y, so N₀=N_X+N_Y.

X:Y=1:7 gives N/(N₀)=1/8=(1/2)³.

So n=3 half-lives have elapsed.

t=3×20.

t=60 yr.

Why the other options are wrong

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