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## Main Question or Discussion Point

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!

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!