Question

A patient is injected with a radioactive tracer isotope with a half-life of 2.5hr. If the initial activity is 7.3kBq, what is the activity 3.5hr later?

Answer 1

The activity of the radioactive tracer isotope 3.5 hours later is 2.84 kBq.

Step-by-step explanation:

To determine the activity of the radioactive tracer isotope 3.5 hours later, we need to consider the half-life of the isotope. With a half-life of 2.5 hours, we can calculate the fraction of the isotope remaining after 3.5 hours using the formula:

Remaining fraction = (1/2)^(time elapsed / half-life)

Substituting the values into the formula, we get:

Remaining fraction = (1/2)^(3.5/2.5) = 0.3906

To find the activity 3.5 hours later, we multiply the remaining fraction by the initial activity:

Activity 3.5 hours later = Remaining fraction * Initial activity = 0.3906 * 7.3 kBq = 2.84 kBq