The specific activity of a radioisotope increases if its half-life:

The specific activity of a radioisotope is defined as the activity per unit mass of the radioactive material. This activity refers to the rate at which disintegrations occur, measured in becquerels or curies.

When the half-life of a radioisotope decreases, it means that the isotope decays more rapidly. A shorter half-life results in a greater number of disintegrations occurring over a given period of time compared to an isotope with a longer half-life. Because activity is a function of how many atoms are decaying per unit time, a decrease in half-life directly translates to an increase in activity at any given mass of the radioisotope.

Thus, since specific activity is calculated as activity per mass, if the activity increases while the mass remains constant, the specific activity must also increase. This is why a decrease in half-life leads to an increase in the specific activity of the radioisotope.