The organelle that controls what enters and leaves the nucleus is the nuclear envelope.

Here's why:

* Structure: The nuclear envelope is a double membrane that surrounds the nucleus. It has pores that act like gates.

* Function: These pores are selective and only allow certain molecules to pass through. This is essential for regulating the flow of information between the nucleus and the cytoplasm.

* Importance: The nucleus contains the cell's DNA, the blueprint for protein synthesis. The nuclear envelope ensures that only the necessary components (like RNA and proteins involved in transcription and translation) can enter the nucleus, and that the DNA stays protected inside.

So, while the nucleus itself is the "brain" of the cell, the nuclear envelope is the gatekeeper, ensuring the right molecules go in and out.