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What do you mean by parallel? if you mean electrons traveling in the same direction in a single orbital, this is not possible as electrons must always be in an opposite spin as stated by Pauli's exclusion principle. The hunds rule states that electrons will fill different orbitals within a subshell each with parallel spin (so 1 electron in each orbital for now, all with the same spin) and once there are enough electrons, it will then fill an orbital which will bring the number to 2e- in one of the orbitals, and this is when the electrons in a single orbital have opposite spin.
The parallel electrons in Hund's rule is just stating that when distributing electrons into different orbitals, every electron in the half-filled orbitals have the same spin (like all three electrons in the 2p^3 subshell) would be either spin-up (+1/2) or spin-down(-1/2). This is because electrons with parallel spins in different orbitals decreases electrostatic repulsion between them, making them more stable.
Hund's Rule is saying that electrons will fill the orbitals alone before doubling up. An orbital can house 2 electrons spinning in opposing directions, however each orbital will fill with one singular electron before 2 occupy the same one. To draw an analogy: if a house has 3 rooms and a family with 2 children moves in, the two kids are more likely to have their own separate rooms before sharing; they'll only share if more kids (electrons) move in.
According to Hund, electrons in the ground state, which is the lowest energy electron configuration, would finally have electrons become parallel. Hence, each orbital of the sub shell is occupied with electrons of parallel spin.
Electrons would be parallel when ground state electrons would fill two or more orbitals before pairing together in the same orbital. This means that the electrons in each orbital would have the same spin rather than when 2 electrons are in the same orbital and when they have opposite spins.
Hund's Rule states that due to electron repulsion electrons in the same subshell, l, will occupy different orbitals with parallel spins and are unpaired. Paired electrons have opposite spins and are in the same orbital.
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