Chapter 11.6, Problem 55E

To determine

Find the time for 2.8 micro curies in the patient's thyroid.

Answer to Problem 55E

  $324hours$

Explanation of Solution

Given information:

Nuclear medicine technologists use the iodine isotope I-131, with a half-life of 8 days, to check thyroid function of patients. After ingesting a tablet containing the iodine, the isotopes collect in a patient's thyroid, and a special camera is used to view its function. Suppose a patient ingests a tablet containing 9 micro curies of I-131. To the nearest hour, A micro curie is a measure of radioactive.

Calculation:

Consider, the formula for time period, $N=N_o{\left(\frac{1}{2}\right)}^t$ ,

Here $N$ is final value and $N_o$ is the initial value and $t$ is the time period,

  $\begin{array}{l}N=N_o{\left(\frac{1}{2}\right)}^t\\ \frac{N}{N_o}={\left(\frac{1}{2}\right)}^t\\ take\log onbothsides,\\ \log \frac{N}{N_o}=\log {\left(\frac{1}{2}\right)}^t\\ \log \frac{N}{N_o}=t\log \left(\frac{1}{2}\right)\\ t=\frac{\log \frac{N}{N_o}}{\log \left(\frac{1}{2}\right)}\end{array}$

Conclude that the time needed to get to $2.8\mu curie$ in the patients thyroid is,

  $1.6845\times halflife=1.6845\times 8\times 24=324hours$

Hence, the time for 2.8 micro curies in the patient's thyroid is $324hours$ .