**Core Concept**
Radiotherapy, a form of cancer treatment, uses ionizing radiation to damage or destroy cancer cells. The primary mechanism involves inducing double-strand breaks in DNA, leading to cell death. However, radiotherapy can also cause damage to surrounding healthy tissues, resulting in various complications.

**Why the Correct Answer is Right**
The first complication after radiotherapy is often mucositis, characterized by inflammation and ulceration of the mucous membranes lining the mouth, throat, and gastrointestinal tract. This occurs due to the rapid division of epithelial cells, which are more susceptible to radiation-induced damage. The resulting inflammation and ulceration can lead to pain, difficulty swallowing, and increased risk of infection.

**Why Each Wrong Option is Incorrect**
**Option A:** **Dryness of the mouth** (xerostomia) is a common side effect of radiotherapy, particularly for head and neck cancers, but it is not the first complication. Xerostomia occurs due to damage to the salivary glands.
**Option B:** **Hair loss** is a common side effect of radiotherapy, particularly for cancers in the head and neck region. However, it is not the first complication, as hair loss typically occurs later in the treatment course.
**Option C:** **Fatigue** is a common side effect of radiotherapy, but it is not a direct complication of the treatment. Fatigue can be caused by various factors, including the cancer itself, treatment-related side effects, and underlying medical conditions.

**Clinical Pearl / High-Yield Fact**
Mucositis is a dose-limiting toxicity of radiotherapy, and its prevention and management are crucial to maintaining patient quality of life during treatment.

**Correct Answer: A. Mucositis**