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The quantum number that would be different between the dxy and dx2-y2 orbitals is the magnetic quantum number (m_l). Both orbitals belong to the same principal quantum number (n) and azimuthal quantum number (l = 2 for d orbitals), but they have different values of m_l: dxy has m_l = -2, while dx2-y2 has m_l = +2. This difference in magnetic quantum number reflects their distinct spatial orientations in the d subshell.
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