A gram of radioactive material has a half-life of one year. After four years how much radioactive material will be left...0g, 1/2g, or 1/4g?

None of the above. The answer one-half to the fourth power.

To determine how much radioactive material will be left after four years, we can use the concept of exponential decay.

The half-life of a substance is the amount of time it takes for half of the initial quantity to decay. In this case, the half-life of the radioactive material is one year.

After the first year, half of the gram of radioactive material will remain (1/2g). After another year, half of that remaining amount will decay, leaving us with 1/4g.

However, since we are looking for the amount after four years, we need to continue this process. After the third year, half of the 1/4g will decay, leaving us with 1/8g. Finally, after the fourth year, half of the 1/8g will decay, resulting in 1/16g.

Therefore, after four years, there will be 1/16g of radioactive material left, which is not one of the given options you provided.