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how can one carbon atom bond with four hydrogen atoms based on their valence electrons
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GPT-5 mini
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Short answer: by sharing electrons. Carbon has 4 valence electrons and needs 4 more to complete an octet; each hydrogen has 1 valence electron and needs one more to fill its 1s shell. Carbon forms four single (covalent) bonds with four hydrogens (methane, CH4), each bond a shared pair of electrons (one from C, one from H). That gives carbon 8 electrons around it and each hydrogen 2 electrons.
A little more detail (why four equivalent bonds): in its ground state carbon is 1s2 2s2 2p2 (four valence electrons). To form four equivalent bonds carbon promotes one 2s electron into an empty 2p orbital and then hybridizes the 2s and three 2p orbitals into four sp3 orbitals. Each sp3 orbital overlaps with a hydrogen 1s orbital to make a sigma bond. The geometry is tetrahedral with bond angles ≈ 109.5°.
If you want, I can draw the Lewis-dot picture or show the orbital diagram.
A little more detail (why four equivalent bonds): in its ground state carbon is 1s2 2s2 2p2 (four valence electrons). To form four equivalent bonds carbon promotes one 2s electron into an empty 2p orbital and then hybridizes the 2s and three 2p orbitals into four sp3 orbitals. Each sp3 orbital overlaps with a hydrogen 1s orbital to make a sigma bond. The geometry is tetrahedral with bond angles ≈ 109.5°.
If you want, I can draw the Lewis-dot picture or show the orbital diagram.
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