**Core Concept**
Pulmonary embolism (PE) can occur in patients with immobilization due to increased coagulability of blood, leading to the formation of blood clots. These clots can dislodge and travel to the lungs, causing a PE.

**Why the Correct Answer is Right**
The patient's history of immobilization for a fracture femur increases the risk of developing a deep vein thrombosis (DVT), which can then break loose and travel to the lungs, causing a pulmonary embolism. The sudden onset of chest pain and hemoptysis in a patient with a history of recent immobilization is highly suggestive of a PE. The ECG finding of S1 Q3 T3 pattern is also consistent with a PE, which can cause acute right heart strain and subsequent electrocardiographic changes.

**Why Each Wrong Option is Incorrect**
* **Option A:** This option is likely not relevant to the patient's presentation of sudden onset chest pain and hemoptysis. While it is possible for a patient with a history of immobilization to develop a PE, the other options listed do not directly relate to the patient's symptoms.
* **Option B:** This option is incorrect because it does not directly relate to the patient's symptoms of sudden onset chest pain and hemoptysis. While a PE can cause hemoptysis, the other options listed do not provide a clear diagnosis for the patient's symptoms.
* **Option C:** This option is incorrect because it does not directly relate to the patient's symptoms of sudden onset chest pain and hemoptysis. While a PE can cause chest pain, the other options listed do not provide a clear diagnosis for the patient's symptoms.

**Clinical Pearl / High-Yield Fact**
The S1 Q3 T3 pattern on ECG is a classic electrocardiographic finding associated with pulmonary embolism. This pattern is thought to be due to the acute right heart strain caused by the PE, which can lead to changes in the electrical activity of the heart.

**Correct Answer:** C. Pulmonary Embolism.