Final answer:
After 3 months, with a half-life of 1 month, you would be left with 8 grams of the initial 64 grams of a radioactive chromium isotope.
Step-by-step explanation:
The question asks how much of a radioactive chromium isotope will remain after 3 months, given a starting amount of 64 grams and a half-life of 1 month. To solve this, we use the concept of half-lives, which tells us that the quantity of a radioactive substance reduces by half for every half-life period that passes.
Since the half-life of the substance is 1 month, after the first month, half of the 64 grams will have decayed, leaving us with 32 grams. Following another month, half of this remaining amount will decay, leaving us with 16 grams. After the third month, another half-life passes, so half of the 16 grams will decay, leaving us with 8 grams.
Therefore, after 3 months, we are left with 8 grams of the radioactive chromium isotope.