To treat thyroid cancer ^131 I is injected in the patient where it rapidly accumulates in the t

step 1 First we'll write the nuclear reaction for the decomposition of iodine 31 through beta emission,

To treat thyroid cancer ^131 I is injected in the patient...

To treat thyroid cancer ${ }^{131} \mathrm{I}$ is injected in the patient where it rapidly accumulates in the thyroid. ${ }^{131} \mathrm{I}$ with a half-life of 8.0 d emits beta particles with an average energy of $182 \mathrm{keV} /$ decay and gamma rays with an average energy of $382 \mathrm{keV} /$ decay. In addition, ${ }^{131} \mathrm{I}$ has a biological half-life in the thyroid of 4.1 d . (a) What is the effective half-life of ${ }^{131} I$ in the thyroid. (b) How many millicuries of this radioisotope should be injected to deliver a 250 Gy dose to the 20 -gram thyroid?

Key Concepts

Physical Half-life

The physical half-life of a radioactive isotope is the time required for half of the nuclei in a sample to undergo radioactive decay. This property is intrinsic to the radioisotope and is independent of biological processes or environmental conditions.

Biological Half-life

The biological half-life describes the time it takes for a living system, such as a specific organ in the body, to eliminate half of a substance through biological processes. This rate depends on the metabolism and the clearance mechanisms of the organism.

Effective Half-life

The effective half-life combines the effects of both the physical decay and the biological elimination of a substance. It represents the overall rate at which the activity of a radioisotope decreases within a biological system. The effective half-life is calculated using the reciprocal of the sum of the reciprocals of the physical and biological half-lives, indicating how quickly the administered activity is reduced by both decay and physiological clearance.

Radiation Emission Types

Radioisotopes can emit different types of radiation, primarily including alpha particles, beta particles, and gamma rays. Beta emissions consist of high-energy electrons or positrons that have moderate penetration ability, while gamma emissions are high-energy photons with high penetration power. Understanding the types and energies of emissions is key for assessing dose distribution and ensuring effective treatment safety.

Radiation Dose and Absorbed Dose

The absorbed dose is a measure of the energy deposited by radiation in a given mass of tissue, typically expressed in Grays (Gy). This concept is essential in radiation therapy, as it quantifies the amount of energy absorbed per unit mass and determines the level of therapeutic effect or potential tissue damage.

Activity Measurement and Unit Conversions

Radioactivity is often quantified in units such as curies (Ci) or becquerels (Bq), with subunits like millicuries for practical medical dosages. Understanding these units and converting between them is crucial in calculating the amount of radioactive material needed to deliver a specific dose in a clinical setting.

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