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Electron promotion happens when an electron that used to be in an s orbital is pushed up to a higher energy level to allow for hybridization. For example, carbon has two electrons in 2s and two electrons in 2p. To hybridize, one electron is pushed from 2s up to 2p. Now there is one electron in 2s and one electron in each of the 2p orbitals. This the orbitals to hybridize, creating three sp3 orbitals that can participate in bonding. In other words, hybridization could not happen without an electron being promoted. So they do go hand in hand. But if you have an element like neon, which can't form bonds, it's not going to hybridize, since hybridization only happens to allow for bonding. So not all atoms with s and p orbitals will hybridize.
Electron promotion is related to hybridization. The hybridized orbital has both s characteristics and p characteristics. Its energy is between the s orbital and the p orbital. As a result, the electron promotion is essential for s orbital electrons to promote to hybridized orbital with higher energy.
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