How to Calculate Percentage of Eliminated Isotopes

Question:

A radioactive isotope has a physical half life of 15.5 h. In 36.0 hours the body will eliminate half of the isotope. After 53.0 hours, what percentage of the original isotopes will have been eliminated?

Answer:

After 53.0 hours, around 75% of the original radioactive isotopes will have been eliminated from the body due to both radioactive decay and body's elimination.

To calculate the percentage of eliminated isotopes after 53.0 hours, we need to consider both the decay of the isotope and the elimination by the body. The half-life of the radioactive isotope is 15.5 hours, which means that after every 15.5 hours, half of the isotopes decay. In 36.0 hours, the body eliminates half of the remaining isotopes, which results in only 1/4 of the original isotopes remaining in the body after 51.5 hours (36.0 hours + 15.5 hours). This implies that 75% of the original isotopes have been eliminated after 53.0 hours.