Final answer:
The device in question is a solenoid valve, which is an electrically operated valve controlling the flow to the atomizer in an oil burner system.
Step-by-step explanation:
The device being referred to that is electrically operated and controls the flow to the atomizer for oil burners is most likely the solenoid valve. A solenoid valve is a type of electrically actuated valve that opens or closes the passage of fluid when an electric current runs through the solenoid coil. This valve is integral in systems that require precise control of fluid flow, such as in the case of oil burners, where the atomizer is responsible for creating a fine spray of oil for efficient combustion.