**Core Concept**
Iodine-131 is a radioactive isotope of iodine that is selectively taken up by the thyroid gland, allowing for targeted treatment of hyperthyroidism. This property is due to the thyroid gland's ability to concentrate iodine, which is then incorporated into thyroid hormones.

**Why the Correct Answer is Right**
Iodine-131 (I-131) is the most suitable radioisotope for treating hyperthyroidism because it is a beta emitter with a relatively short half-life of approximately 8 days. This allows for a high dose to be delivered to the thyroid gland while minimizing exposure to surrounding tissues. I-131 is selectively taken up by the thyroid gland through the sodium-iodide symporter (NIS), which is highly expressed in thyroid follicular cells.

**Why Each Wrong Option is Incorrect**
**Option A:** This option is incorrect because I-123 is a beta-negative emitter with a much shorter half-life (13.22 hours) and is primarily used for diagnostic purposes, such as thyroid scanning.

**Option B:** This option is incorrect because I-125 is a beta emitter with a very long half-life (59.4 days), making it unsuitable for treating hyperthyroidism due to prolonged radiation exposure.

**Option C:** This option is incorrect because I-129 is a beta emitter with a half-life of approximately 15.7 million years, making it impractical for medical use.

**Clinical Pearl / High-Yield Fact**
It's essential to note that I-131 treatment for hyperthyroidism requires careful dosing and follow-up to avoid potential side effects, such as radiation thyroiditis or secondary malignancies.

**Correct Answer: A. Iodine-131**