how does oxidative phosphorylation work in aerobic respiration

So this part is the last stage of respiration and you will probably ask yourself whats the point of all the NADH and FADH produced during the previous reactions ie Glycolysis producing (per glucose molecule) 2 NADH. Link reaction- 2 NADH. Krebs cycle - 6 NADH and 2 FADH. These coenzymes are actually really useful for the last part. So looking at this chemically NAD has become NADH by gaining a hydrogen right and the same for FADH. During oxidative phosphorylation which takes place in the Cristae ( folding of the inner mitochondrial membrane), the reduced coenzymes NADH and FADH become reoxidised as they donate there hydrogen atoms, which then will split to protons and electrons however it is important to note this reoxidation occurs in the matrix. The electrons then go down these electron carriers which are proteins embedded in the Cristae and because a series of redox reactions occur between the electron carriers and the electrons, a small amount of energy is released because the electrons are essentially moving down energy levels. this energy is used to pump the protons which are currently in the matrix, across the Cristae to the inter membrane space which is between the inner and outer membrane. The inner membrane is impermeable to protons so the protons are forced to go through this enzyme called ATP synthase (protein) embedded in the Cristae, the protons move through ATP synthase via a process called chemiosmosis due to the chemiosmotic gradient formed across the inner mitochondrial membrane. As they flow through ATP synthase catalyses the addition of ADP + P = ATP. so finally why is it called oxidative phosphorylation?? because oxygen is needed at the end. oxygen acts as the final electron carrier, oxygen combines with the electrons from the E transport chain and some protons to finally form water. 02+4e+4H+_____ 2H20