Element X is a radioactive isotope such that every 82 years, its mass decreases by half. Given that the initial mass of a sample of Element X is 8900 grams, how long would it be until the mass of the sample reached 7700 grams, to the nearest tenth of a year

17 years

Explanation:

Expression for rate law for first order kinetics  for radioactive substance is given by:

where,

k = rate constant

t = age of sample

a = let initial amount of the reactant

a - x = amount left after decay process  

a) for completion of half life:

Half life is the amount of time taken by a radioactive material to decay to half of its original value.

b) for 8900 g of the mass of the sample to reach  7700 grams

Thus it will take 17 years