Final answer:
The false statement about the half-life of a radioactive isotope is that a longer half-life always indicates a more radioactive (or hazardous) isotope. In fact, radioactivity is higher in isotopes with shorter half-lives because they decay more rapidly.
Step-by-step explanation:
The statement concerning the half-life of a radioactive isotope that is FALSE is the idea that the half-life is directly related to the level of radioactivity in the sense of overall hazard. While it might seem intuitive that an isotope with a longer half-life would be more radioactive, this is not necessarily the case.
Radioactivity is a measure of the decay rate of a radioactive substance, and it is not solely determined by its half-life.
Isotopes with shorter half-lives decay more rapidly, meaning a greater number of radioactive decays per unit time, thus they are often more 'radioactive' in the sense of activity level. For instance, an isotope with a half-life of a few days might emit radiation more intensely than one with a half-life of many thousands of years.
Consequently, a short half-life generally indicates high radioactivity, making it more hazardous over a short period compared to an isotope with a longer half-life that decays more slowly.