Electrons Fill the Rooms by Rules
When many electrons crowd into one atom, they do not sit just anywhere. They fill the rooms by fixed rules: the lowest-energy room first (the aufbau rule), at most two electrons with opposite spins per room (Pauli), and one electron in each room of a level before any room gets a pair (Hund). Add the shielding of an outer electron by the inner ones, and the twist that 4s fills before 3d, and the order of the periodic table starts to make sense. This lesson is not about the shape of a single orbital. It is the story of how many electrons share their seats by rule.
Add electrons one at a time and each one always drops into the lowest-energy room that still has space. That is the aufbau rule. A room holds at most two electrons, and when it does their spins must point opposite ways, the Pauli exclusion principle. As you add more, they fill in the order 1s, 2s, 2p, 3s, and so on, and you can watch the configuration string 1s² 2s² 2p⁶ grow below.
When a level has several rooms, such as the three rooms of a p subshell, electrons spread out one per room before any of them pairs up. On top of that, these unpaired spins line up parallel to one another. This is Hund's rule. Toggle to the wrong filling, where two electrons are crammed into one room, and you see that the spread-out version has a larger total spin S and a lower energy, the true ground state. Because electrons repel one another, it pays to sit in separate rooms when they can.
The space where each room's electron actually lives has its own shape. The 1s is a round ball, the 2p is a two-lobed dumbbell, and the 3d is a four-leaf clover. What you see here, ψ and its square |ψ|², is the probability cloud where the electron may be found, and this lesson lets you rotate it as a three-dimensional solid. The quantum-mechanics area's hydrogen-orbital lesson shows the very same thing as flat two-dimensional cross-sections instead. Drag to spin it and switch orbitals to watch how the sign of ψ, marked by color, and the solid shape change.
An outer electron does not feel the full positive charge of the nucleus, because the inner electrons between it and the nucleus screen part of that charge. So the effective nuclear charge the outer electron actually feels is Zeff = Z minus S, the proton count Z less the amount of shielding S. Slide the inner electrons up and Zeff drops, while the orbital radius of the less strongly pulled outer electron grows, roughly r proportional to n squared over Zeff. The more shielding there is, the farther out the outer electron drifts.
The order of the energies depends on the atomic number Z. As you raise Z, the energy bars for 4s and 3d both drop, but 3d drops more steeply, so at some point the two cross. That is why in potassium (Z=19) and calcium (Z=20) the 4s lies below the 3d and fills first, while from scandium (Z=21) onward the 3d has dropped below the 4s and begins to fill. This reordering sets exactly where the transition metals begin. Slide Z and find the moment when the two bars swap places.