Radioactivity is a phenomenon in which unstable atoms decay, emitting radiation and transforming into another element. Radioactive elements have an inherent instability that causes them to naturally break down over time. This process is known as radioactive decay. The rate of decay for any given element is characterized by its half-life, which is the amount of time it takes for half of the original amount of the element to decay.

In this case, we are looking at a certain radioactive element with a half-life of 5 hours. With this information, we can determine how much of the original mass will be left after 2 days (48 hours). To do so, we need to calculate how many half-lives have passed during that time period: 48 hours / 5 hours = 9.5 half-lives.

Since each successive half-life reduces the mass by one half, after nine and a half such reductions our initial 6,470 grams would be reduced to 1/2^9 x 6 470 grams = 0.098 grams = 98 milligrams. Therefore after two days there would be 98 milligrams (0.098 grams) left from the initial 6,470 grams of radioisotope present when it was first measured.

This type of calculation can be used to answer questions related to other types of radioactive substances as well; all that needs to be known is the specific characteristics associated with their decay rate – namely their particular half-life(s). Knowing these details allows us to accurately predict how much material will remain at any given point in time once it has begun decaying; further calculations additionally allow us to estimate future amounts if needed or desired as well..

Understanding and being able to utilize this concept can prove useful in many different situations and industries – medical professionals may use it when diagnosing diseases or creating treatments involving radioactive materials; scientists researching new substances may use it when attempting understand what happens during complex processes involving isotopes; engineers may find applications while designing equipment that could house or interact with such materials too; and so on