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I am a beginner and am learning about atomic structure and I am getting confusions regarding the aufbau principle.

It is said that the electrons will be filled first in lowest available energy level. But according to aufbau principle electrons are filled in $\mathrm{4s}$ orbital before filling the $\mathrm{3d}$ orbital. Similarly,electrons are filled in $\mathrm{5s}$ before $\mathrm{4f}$.

But I am also taught that if $n$(principle quantum number) increases,the size of the orbital also increases. By size I mean the maximum distance from the nucleus.

So accordingly, $\mathrm{4s}$ orbital should have greater size than $\mathrm{3d}$. Similarly $\mathrm{5s}$ should have greater size than $\mathrm{4f}$. Hence $\mathrm{4s}$ as well as $\mathrm{5s}$ are farther from nucleus as compared to $\mathrm{3d}$ and $\mathrm{4f}$ respectively. Thus they have more total energy and hence electrons should be filled in $\mathrm{3d}$ and $\mathrm{4f}$ before $\mathrm{4s}$ and $\mathrm{5s}$ respectively.

But the above stated doesn't happen. My confusion is, "Why isn't this line of thinking correct?"

Here is a diagram depicting that $\mathrm{4s}$ is bigger than $\mathrm{3d_{xy}}$. Orbitals

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    $\begingroup$ It seems like you are confused about why the principal quantum number is sometimes secondary to the angular number with respect to energy ordering. If rephrased, it's a reasonable question, why is 4s lower in energy than 3d, for instance. It's answered entirely in: chem.libretexts.org/Bookshelves/… . $\endgroup$ – Bertram May 12 at 17:21
  • $\begingroup$ @Bertram,thanks for the link you shared,but it still does not clear my confusion about why is this so,the website you mentioned shows the aufbau rule and its exception,but why does it happens so,its not yet clear to me!though I thank for your contribution $\endgroup$ – Dheeraj Gujrathi May 12 at 18:03
  • $\begingroup$ The maximum distance of an orbital doesn't mean that the electron is always going to be on the border. You are thinking in terms of Bohr's model, which is wrong. $\endgroup$ – Nisarg Bhavsar May 13 at 5:50
  • $\begingroup$ @Nisarg Bhavsar,could you please elaborate where am I understanding it wrong?I am trying to understand and had searched all way long on internet but didn't find anything! Please explain more about the 'border' sentence too. $\endgroup$ – Dheeraj Gujrathi May 13 at 7:58
  • $\begingroup$ The quantum orbitals are not orbits which an electron takes while "revolving" around the nucleus. It's just an area where the probability of finding an electron is high. In fact the electrons do not "revolve" around the nucleus. An electron is just everywhere in the atom until we measure it's position. So, talking about the "border radius" and relating it with the electrostatic binding energy with the nucleus doesn't hold water in a system with more than one electron. $\endgroup$ – Nisarg Bhavsar May 13 at 9:38

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