**Core Concept**
Prophylactic vitamin A supplementation is a crucial public health measure to prevent vitamin A deficiency-related disorders, such as night blindness, in infants and young children. Vitamin A plays a vital role in maintaining the integrity of epithelial tissues and immune function.

**Why the Correct Answer is Right**
The recommended initial dose of vitamin A for prophylaxis in a 9-month-old child is 100,000 IU (International Units). This dose is administered to children between 6 and 11 months of age as part of the World Health Organization's (WHO) Expanded Programme on Immunization (EPI). The high dose is necessary to rapidly replenish vitamin A stores in the liver, which are essential for maintaining immune function and preventing deficiency-related disorders.

**Why Each Wrong Option is Incorrect**
**Option A:** 50,000 IU - This dose is too low for a 9-month-old child and would not provide adequate protection against vitamin A deficiency.
**Option B:** 200,000 IU - This dose is higher than the recommended initial dose and may cause adverse effects, such as headache or nausea.
**Option C:** 50,000 IU monthly - This is an incorrect dosing schedule and would not provide the necessary rapid replenishment of vitamin A stores.

**Clinical Pearl / High-Yield Fact**
Remember, the WHO recommends vitamin A supplementation in children between 6 and 11 months of age as part of the EPI, with a dosing schedule of 100,000 IU at 9 months and 6-12 months.

**Correct Answer:** A. 100,000 IU.