Final answer:
The client with a fractured leg and in a cast is at the highest risk for pulmonary embolism due to increased likelihood of deep vein thrombosis from immobility.
Step-by-step explanation:
The client at the greatest risk for a pulmonary embolism (PE) is the one who has a fractured leg and is in a cast (Option C). PE is a serious condition where a blood clot breaks off, travels through the blood vessels, and lodges in a pulmonary artery. This can lead to significant lung damage or even death due to the disruption of the pulmonary circulation. Clients with limited mobility, such as those with a fractured leg, are at higher risk because immobility can lead to deep vein thrombosis (DVT), which is a precursor to PE.