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How to compare energy levels in $\ce{sp, sp^2, sp^3}$ orbitals?

Since a higher energy level implies lower stability, an $\ce{sp-sp}$ bond must have the lowest energy level, since it is formed by the overlap of one sigma and two pi bonds in total, more than those in $\ce{sp^2-sp^2}$ or $\ce{sp^3-sp^3}$. Hence, $\text{energy level(}\ce{sp < sp^2 < sp^3}\text{)}$.

Is my calculated trend correct? If so, then is this the intended reasoning? If not, then why?

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How to compare energy levels in $\ce{sp, sp^2, sp^3}$ orbitals?

Background

  • Electrons in an atomic $\ce{2s}$ orbital will be lower in energy than electrons in an atomic $\ce{2p}$ orbital since the s orbital is closer to the nucleus.
  • When we describe a hybrid orbital as $\ce{sp^n}$, this is really a shorthand notation for $\ce{s^1p^n}$, which means that the orbital is made up from 1 part s orbital and n parts p orbital.

Analysis

As the "n" in $\ce{sp^n}$ grows larger we will have more p character and less s character in the hybrid orbital and, as explained above, it will consequently be higher in energy. So an $\ce{sp}$ hybrid orbital that has 50% s character will be lower in energy than an $\ce{sp^3}$ orbital which only contains 25% s character.

The energy ordering you proposed in your question is correct: $\ce{sp < sp^2 < sp^3}$.

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