Hydrogen’s electron cloud only has one “connector” for bonding. Oxygen has two.
More specifically, hydrogen’s electron cloud is one electron away from full, while oxygen’s is two. Atoms don’t like to have partially filled electron clouds, and will try to complete them. In the case of hydrogen and oxygen, this means bonding.
When two atoms bond, they each share two electrons, one from each. But, each electron in the bond takes up space in both atoms’ electron clouds. So, forming a bond adds an electron to both atoms’ electron clouds.
Hydrogen bonds with oxygen, and it’s full. But, the oxygen still has one unfilled slot, so it can bond to one more atom. This can be another hydrogen (in the case of water), another oxygen (in the case of hydrogen peroxide), or whatever.
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