A radioactive isotope of mercury,, decays into gold, , with a decay constant of 0.0108 . (a) We have to calculate its half-life, (b) the fraction of the original amount that will remain after three half-lives, after 10 days.

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(a)

A radioactive isotope of mercury,, decays into gold, , with a decay constant of 0.0108 . Half-life and decay constants by definition are related as

As ,

(b)

The fraction of the original amount that will remain after three half-lives will be

And, the fraction of the original amount that will remain after 10 days will be