Question

After 22hours only 5mg of radioactive material remains in a patient. If the half-life of the sample is 4.4 hours, how much of this material was originally injected into the patient?

Answer 1

The patient was originally injected with 160 mg of radioactive material. This calculation is based on the half-life of the material being 4.4 hours and using the number of half-lives (5) that have passed to determine the initial amount.

Step-by-step explanation:

To determine how much radioactive material was originally injected into the patient, we can use the concept of half-life from the field of radioactive decay. The half-life of a substance is the time it takes for half of the radioactive material to decay. Given that the half-life of the radioactive material in this case is 4.4 hours and 5 mg remains after 22 hours, we can calculate the original amount.

First, we determine the number of half-lives that have passed:

Number of half-lives = Total time elapsed / Half-life time = 22 hours / 4.4 hours = 5

Using the principle that after each half-life, half of the remaining material will have decayed, we can work backwards:

1. After 4th half-life (4.4 * 4 hours): 5 mg * 2 = 10 mg
2. After 3rd half-life (4.4 * 3 hours): 10 mg * 2 = 20 mg
3. After 2nd half-life (4.4 * 2 hours): 20 mg * 2 = 40 mg
4. After 1st half-life (4.4 * 1 hours): 40 mg * 2 = 80 mg
5. Initial amount (before any decay): 80 mg * 2 = 160 mg

Therefore, the patient was originally injected with 160 mg of radioactive material.