**Core Concept:**

The question is asking about radioisotopes, which are isotopes of elements that possess radioactivity and are used in various medical applications, particularly in nuclear medicine. In the context of the question, we are dealing with two types of radiotherapy: Teletherapy and brachytherapy. Teletherapy involves the use of external radiation sources to deliver radiation to the tumor, while brachytherapy relies on the use of radioactive sources placed directly into or near the tumor for localized radiation therapy.

**Why the Correct Answer is Right:**

The correct answer should be a radioisotope commonly used in both Teletherapy and Brachytherapy. In this case, the correct answer is **Cobalt-60 (60Co)**. Cobalt-60 is a gamma-emitting radioisotope with a half-life of 5.27 years, which makes it suitable for both types of radiotherapy due to its stability and penetrating power.

**Why Each Wrong Option is Incorrect:**

A. Cobalt-59 (59Co) is a different radioisotope with a half-life of only 77.2 days, which is too short for practical use in long-term radiation therapy.
B. Iridium-192 (192Ir) is a beta-emitting radioisotope, not gamma-emitting like Cobalt-60, making it unsuitable for Teletherapy and Brachytherapy.
D. Iodine-131 (131I) is a beta-emitting radioisotope, similar to Iridium-192. It is primarily used in nuclear medicine for diagnosis and therapy, not for radiotherapy.

**Clinical Pearl / High-Yield Fact:**

Cobalt-60 (60Co) is a highly versatile radioisotope used in various medical applications, including cancer treatment. Its gamma-emitting nature allows for deep penetration and minimal damage to surrounding healthy tissues. Cobalt-60 is commonly used in:

1. **Teletherapy:** External beam radiation therapy, where a device delivers gamma rays to the tumor from a distance, ensuring that healthy tissues are spared from radiation exposure.
2. **Brachytherapy:** Internal radiation therapy where radioactive sources are placed directly into or near the tumor, allowing for high radiation doses to the target area while minimizing damage to surrounding tissues.

By understanding the correct answer and the reasons behind the incorrect options, students can recognize the importance of choosing the right radioisotope for specific medical applications and the effects of different types of radiation emitted by the isotopes. This knowledge is crucial for medical professionals involved in radiotherapy, dosimetry, and patient management.