How much material will be left if a radioactive isotope has a half life of 1.3 billion years in 3.9 billion years?
Half-life (t½) is the amount of time required for a quantity to fall to half its value as measured at the beginning of the time period.
In this question (t½) is 1.3 billion years, which means that after 1.3 billion years half of the sample would have decayed and half would be left as it is. let us say that we have 90 mg of sample in the beginning , you can assume any amount.
After years ( first half life, 1.3 billion years) 90 /2 = 45 mg decays and 45 mg remains left.
After another 1.3 billion years ( two half lives or 2.6 billion years) 45 /2 = 22.5mg decays and 22.5 mg remains left .
After another 1.3 billion years ( three half lives or 3.9 billion years) 22.5 /2 = 11.25mg decays and 11.25g remains left.
after three half lives or 3.9 years, 11.25 mg will be left.