After falling on the back of head , does ct scan shows all possible kinds of damage ? i mean if the ct scan shows nothing there's no problem ?

Any Symptoms?: If you are asypmtomatic, no pain, dizziness, irritability, nausea, double vision, discoordination, memory issues, that are new since the injury then you should be ok. Ct scanning and mri's do not eliminate the possibility of concussion which is a clinical diagnosis, not a radiographic one.

Usually: Ct scans are excellent in looking for traumatic changes to the brain and skull. If the ct scan is normal, you are likely fine. There are, however, subtle changes that can be seen by MRI in some people with head trauma that are missed by ct. If you have new neurologic problems after head trauma, it is best to discuss this with your doctor to see if more imaging is indicated.