Final answer:
The nurse should perform synchronized cardioversion for a client with hemodynamically unstable supraventricular tachycardia, considering the patient's low blood pressure and very high heart rate.
Step-by-step explanation:
A nurse caring for a client with supraventricular tachycardia (SVT) with hemodynamic instability, as evidenced by a heart rate of 200 beats per minute (bpm), low blood pressure (BP) of 78/40 mm Hg, and a high respiratory rate of 30 breaths per minute, must take immediate action. The priority in this case, due to the client's unstable status reflected by the blood pressure, is to perform synchronized cardioversion, assuming that rapid response and advanced resuscitation equipment and personnel are available. Other interventions like administering atropine, encouraging Valsalva maneuver, and initiating chest compressions might be appropriate in different scenarios, but with the given clinical signs, synchronized cardioversion is indicated to restore a normal heart rhythm.
Medications such as beta-blockers may be considered after cardioversion or if the patient were stable. Atropine is generally used for symptomatic bradycardia and not for SVT. The Valsalva maneuver can be attempted if the patient is stable, to help reduce heart rate but is not the priority in hemodynamically unstable patients. Chest compressions are initiated when the patient is unresponsive and pulseless, which does not apply to this scenario.