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I am told that for these two molecules, one of them is not as resonance stabilized as the other. Apparently it's the chlorine one, and it's because of the mismatch in the size of chlorine and carbon. This makes sense prima facie, but can someone confirm this is true? I can see how carbon and nitrogen have similarly sized p orbitals and thus have good overlap, and how chlorine and carbon might have poor p orbital overlap, like a BB pellet with a basketball.

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Yes, your analysis is accurate. The nitrogen is donating electrons through a 2p orbital which is similar in size to the carbon and oxygen 2p orbitals. The chlorine is donating electrons through a 3p orbital, which is significantly larger than the second row elements' 2p orbitals.

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Yes, this is true. The $\pi$ overlap between a valence $\ce{p}$ orbital of a second row element and one of a higher row element is much smaller than the $\pi$ overlap between two second row elements. One reason is that the bond length is generally higher when higher row elements are involved (due to their size). Another reason is, that the $3 \ce{p}$ or $4 \ce{p}$ orbitals are much more diffuse than the $2 \ce{p}$ orbitals. If you want to read deeper into the topic have a look at:

[1] W. Kutzelnigg, Angew. Chem. Int. Ed. Engl., 23, 272 (1984).

[2] N. C. Norman, Polyhedron, 12, 2431 (1993).

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