Final answer:
The half-life of the radioactive substance is 26 hours.
Step-by-step explanation:
The half-life of a radioactive substance is the time it takes for half of the original amount of the substance to decay. In this case, the substance decays to one sixth of its original amount in 13 hours. To find the half-life, we need to find the amount of time it takes for the substance to decay to half of its original amount.
Since the substance decays to one sixth of its original amount in 13 hours, it would decay to one half of its original amount in twice the amount of time, which is 26 hours. Therefore, the half-life of the substance is 26 hours.