Final answer:
The first action the nurse should take when a child with pertussis is admitted to the pediatric unit is to place the child on droplet precautions.
Step-by-step explanation:
When a child with a diagnosis of pertussis (whooping cough) is admitted to the pediatric unit, the nurse's first action should be to place the child on droplet precautions. Pertussis is highly communicable through droplet transmission, and placing the child on droplet precautions helps to minimize the risk of transmission to others. Administering antibiotics and obtaining a sputum culture are actions that may be taken later, after the child has been placed on precautions and any necessary respiratory isolation measures have been initiated.