Can you guys tell me how big can the gap be from a palate expander?

Depends: Depending on the specific palatal expander, anywhere from 8-12 mm.

3-4 mm max: A rapid palatal expander will be used in the mouth approximately two weeks with actively turning the key. The screw in the expander controls the horizontal translational movement of the expander, which is about 3-4 mm horizontally. The amount of horizontal expansion actually can be designed by the dentist and the lab (usually the lab).

Depends on screw: Space between top front teeth can be as much as 8-12mm after expansion, and then the space will spontaneously close (although the palatal expansion will not) over the next few months. Depends on size of the expansion screw, anatomy of the palate, placement of the screw, age of the patient, and many other factors. Space is good, it shows the appliance is effective.