Question

Radioisotopes are often used in diagnostic imaging for detecting disease. The isotope 131I (iodine-131), which has a half-life of 8.02 days, is used in nuclear medical imaging. What percentage of the original activity in the sample remains after 17.5 days

Answer 1

Answer: Approximately 22.04% of the original.

Step-by-step explanation: Radioisotopes, like iodine-131, have unstable nuclei. To become stable, they eject some particle (alpha or beta) or energy (gama).

Half-life is a time for half of the substance to decay. Activity is rate of decay, i.e., the number of decays per unit time.

Half-life and Activity are related by the following:

`A=A_(0).(1)/(2^(n))`

where

A is activity

`A_(0)` is initial activity

n is number of half-lives passed in t

For iodine-131, half-live is 8.02, so in 17.5 it has passed:

`n=(17.5)/(8.02)`

n = 2.182

Final activity will be:

`A=(A_(0))/(2^(2.182))`

`A = 0.2204A_(0)`

Which means after 17.5 days, there were 22.04% of the original iodine-101.