Final answer:
The first action a nurse should take when caring for a client with a pulmonary embolism is to administer oxygen therapy to address hypoxemia and stabilize the patient.
Step-by-step explanation:
The first action a nurse should take when caring for a client experiencing a pulmonary embolism is C) Administer oxygen therapy to the client. Oxygen therapy is crucial in managing pulmonary embolism because it helps to address hypoxemia, the lower-than-normal level of oxygen in the blood, a common complication of pulmonary embolism. Ensuring the patient receives adequate oxygen is essential to prevent further complications and to stabilize the patient's condition before other diagnostic procedures, like an electrocardiogram (ECG), or treatments, such as pain medication or a CT pulmonary angiography, are administered.