I am wondering how two orbitals of same n values can be orthogonal, for example how are a 2s and 3s orbital orthogonal? What I understand is a property of orthogonality is the product of the two wave functions integrate to zero over all space. I tried to look at this graphically and categorize overlapping regions as either positive or negative products and then cancel out positive and negative regions to yield zero, but what I am having trouble is that the 3s orbital is larger than the 2s orbital, so how can they possible integrate to zero? If someone could also explain the significance/implications of all orbitals being orthogonal that would be helpful too! I do not understand the importance of orthogonality in orbitals! Thank you!