[Blueberries116]

The following question arises from a set of statements from which I'm asked to state whether they are true or false.

This is as follows:

Indicate which of the following statements are true or false:

1. On [itex]\underset{np}{\underline{\uparrow}\,\underline{\uparrow}\,\underline{\downarrow}}[/itex] there is a transgression to Hund's rule of maximum multiplicity

2. The given box notation [itex]\underset{np}{\underline{\uparrow\,\uparrow}}[/itex] is a transgression to Pauli's exclusion principle.

3. The following configuration [itex]1s^22s^22p^13s^1[/itex] is a transgression to Pauli's exclusion principle.

4. The electron configuration of Silver [itex](Z=47)[/itex] is [itex][Kr]5s^{1}4d^{10}[/itex].

5. Two chemical species with the same number of electrons not necessarily have the same configuration.

Given these statements I found it difficult to make a proper interpretation of what was intended with the fifth and the first option.

The second option is true. As two electrons occupying the same orbital cannot have the same quantum numbers.

The third option is not true due that's not a transgression to Pauli's exclussion principle. But rather to Aufbau's build up principle. Because it states that the electrons will occupy the orbital with the lowest energy possible.

The fourth option is correct, that's the electron configuration of Silver.

But the problem arises from the first option as I don't know if it does make a transgression to Hund's principle of maximum multiplicity?. As I understand there isn't any reason to justify that the electron will always have to be filled with a [itex]m_s=-\frac{1}{2}[/itex]. It only states that the most stable configuration will be the one where electrons fill the most orbitals as possible.

Then the fifth option is a bit hard to understand, as I don't get very clear what's the meaning of chemical species. I'm assuming since this question is related with atomic structure chapter, it is referring to atoms. In the given context ions more specifically, and understood in such way it does say that two isoelectronic atoms will not have the same configuration. But is that possible?. How can it be justified?. Help please!

[mjc123]

Hund's rule of maximum multiplicity states that, when degenerate orbitals are singly occupied, the lowest energy state is the one where the unpaired electrons all have parallel spins. So statement 1 is true.

As to 5, consider for example the configurations of Ca and Ti²⁺.

[Enthalpy]

A resource useful to meditate about spin alignment:
http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/helium.html
the energy levels of para- and ortho-helium, that is, with spins anti- or parallel, one electron as 1s and the other as varied orbitals.

The energy differs much. The interaction of magnetic moments, about as weak as the orbital-spin interaction that defines the fine structure, can't possibly explain it.

Spin alignment changes the energy even when electrons are not on identically named orbitals. So spin alignment matters more than the mere exclusion principle.

Because electrons are fermions, their common wave function ψ(r₁, spin₁, r₂, spin₂) must be antisymmetric, including the comparison between spin₁ and spin₂. It's a mathematical consequence of being fermions, not a force. This implies that the (6-dimensional hyper-) shape ψ(r₁, r₂) differs whether the spins are anti- or parallel. Then the energy differs a lot, due to the proximity with the nucleus and between the electrons.

We use to represent parallel spins as "up", but I understand it only means "all parallel", and they could all be "down" equally well. It's not an interaction with the orbital angular momentum or magnetic field.