# Hund's rules

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## Area of ​​Expertise - Quantum physics

Hund's rules, which were established by Friedrich Hund in 1927, describe the energetic order of the terms belonging to a certain electron configuration of an atom:

1. For terms resulting from equivalent electrons, the term with the highest spin multiplicity is at the lowest energy.
2. If several terms meet this criterion, the term with the highest orbital degeneracy (maximum $L.$) at deepest energy.
3. The energy of the deepest states increases with the $J$Values ​​on if the terms derive from a configuration of a less than half-occupied shell, otherwise it falls off.

## Learning units in which the term is dealt with

### Construction principle of the periodic table45 min.

#### ChemistryGeneral ChemistryPeriodic table

How is the periodic table structured? What are the criteria behind the structure? Wolfgang Pauli was the first to express and prove the principle in words.

### Multi-electron atom: Hamilton operator45 min.

#### ChemistryTheoretical chemistryMore electron atom

Starting from the Hamilton operator for multi-electron atoms or molecules, the Born-Oppenheimer approximation is introduced and the electronic Schrödinger equation is obtained. Finally, important fundamentals of the quantum mechanical treatment of atoms are dealt with, namely electron spin, electron configuration, term symbolism and the division into internal and outer electrons.

The term with the largest multiplicity has the lowest energy.

 Example: In the configuration we expect the order:
The explanation of this rule lies in the spin-spin interaction. Strictly speaking, it is the Coulomb repulsion that is responsible for the energy difference. The symmetrical spin state enforces an antisymmetrical spatial state in which the electrons are on average further apart and therefore less shield each other, which results in a lower energy. The sketches below make it clear why this is so:

These sketches are purely conceptual, they do not show any realistic proportions.

Note that the energies considered here are electrical, potential energies. A negatively charged electron has a negative energy in the vicinity of a positive nucleus, which leads to a bound state. A force between the electrons will counteract this through a contribution of positive potential energy, the electron will be bound more weakly or is higher in the potential energy.

## Experiment 15 - The Resistance Cube II

How do you calculate the resistance of the cube? Simple formulas won't help you here. You need Kirchhoff's rules, Ohm's law and some symmetry considerations.

Look at the schematic illustration of the resistance cube.

• Because of the symmetry, the currents are I.3 = I.4 = I.7 = 1 /3 I.total(Knot rule!).
• The points C. , D. and E. are therefore on the same potential, there UAC = UAD = UAE(Ohm's law!).
• The same applies to the currents (I.5, I.10, I.12) and the potential at the points F. , G and H

Now you connect the dots same potential with each other, so flows no electricity through the cables, as there is no voltage (Rule of stitches!). Have the additional lines no influence on the circuit!

The additional lines are in green drawn. The circuit diagram can therefore be redrawn.

Illustration resistance cube with fictitious connections.

Circuit diagram resistor cube with fictitious connections.

The circuit now consists of one Series connection three Parallel connections. This is easy to calculate.

However, they are Symmetries of a circuit not always as easy to see as with the cube. Therefore, general circuits with the so-called Network analysis calculated.

## CH instruction and rules of conduct

Schoolchildren must be given information and knowledge about safe behavior in the chemistry room. This applies to both the use of the facility and the teaching of hazardous substances. Basically, instructions on how to behave in the specialist room must take place at least every six months. The basis for this can be B. be the departmental regulations.

General rules of conduct:

• Schoolchildren are not allowed to enter chemistry rooms without the supervision of the subject teacher. In principle, you are not allowed to be alone in it.
• Teachers are generally not allowed to leave the subject room during lessons. If, for compelling reasons, a teacher has to leave the room for a short time, the safety measures required to prevent accidents must be taken. Operating a pass-through fume cupboard from the rear is permitted if access is through a door immediately next to it.
• Eating and drinking are prohibited in the specialist rooms. Food and drinks for personal consumption may not be stored in specialist rooms.
• Coats, jackets and bags should be stored outside of the chemistry rooms if possible. Under no circumstances should they be placed on work tables or in traffic routes.
• The pupils are to be informed about
• Location and operation of the electrical emergency stop switch and the central main gas tap
• existing extinguishing equipment (fire extinguisher, extinguishing sand)
• Location and operation of the emergency eye showers
• Escape routes or an existing rescue plan

Experiments on schoolchildren

Experiments on schoolchildren may only be carried out if damage to health is excluded and the hygienic requirements are guaranteed.

Therefore z. B. Prohibited:

• The application of hazardous substances and other substances / mixtures to the skin as well as taste samples
• Taking blood from schoolchildren
• Experiments with ionizing rays
• Experiments with dangerous contact voltages
• Attempts in which the skin comes in contact with very hot or cold media

When picking up electrophysiological signals (EKG, EEG), only devices that comply with the Medical Devices Act or the Medical Device Ordinance or that are operated completely disconnected from the power supply and on which no dangerous contact voltages can occur may be used.

Solo work and supervision

As a rule, pupils are only allowed to carry out experiments in school under the supervision and responsibility of the teachers. The teacher is obliged to supervise the pupils according to the age and maturity of the pupils.

In individual cases, the teacher can let pupils experiment in the school without constant supervision if, based on previous teaching experience with these pupils, they can assume that they will handle the devices and chemicals provided appropriately. Students are not allowed to work alone.

Clothing and footwear

Wear suitable clothing and sturdy, closed-toe shoes when experimenting. The clothing should be as close-fitting as possible and be flame-retardant (made of cotton or mixed fabrics with at least 35% cotton). Pure synthetic fabrics do not meet these requirements.

#### Sources

##### Notes on the guidelines for safety in teaching at general schools in North Rhine-Westphalia

In North Rhine-Westphalia, the Ministry for Schools and Further Education issued the guidelines for safety in teaching at general education schools in North Rhine-Westphalia - RISU-NRW in November 2016. With this decree for the introduction of the RISU-NRW, the school ministry established the hazardous substances officer as a special actor in the hazardous substance management system in schools. The hazardous substances officer is an occupational safety officer within the meaning of Section 13 (2) of the Occupational Safety and Health Act. The teachers, who are officers responsible for hazardous substances and are themselves employees within the meaning of the Hazardous Substances Ordinance, are also responsible for performing the employer's tasks. They fulfill an important multiplier function in the implementation of the regulations from the Hazardous Substances Ordinance in schools.

In North Rhine-Westphalia, the Ministry of Education has issued an independent guideline for safety in teaching at vocational colleges in North Rhine-Westphalia - RISU-BK NRW with the associated manual for the corresponding cross-professional subjects in vocational / vocational schools, so NRW deviates here from the RISU-KMK version away.

## Knot rule (1. Kirchhoff rule)

Let's start with the knot rule, often referred to as Kirchhoff's first rule. The statement behind this is actually quite simple: The current that flows into a node must be exactly the same as the current that flows out. First take a look at the following graphic, underneath you will find explanations.

The arrows pointing to the node mean: The current flows into the node. The arrows away from the node say: The current flows out of the node. The knot rule says that the currents that flow in are as large as the currents that flow out. For our example this means:

The sum of the incoming flows is the same as the sum of the outgoing flows. If you know three of the four currents in our example, you can calculate the fourth.

## Determine electron configuration + example

Knowledge of orbitals and quantum numbers is the basis for determining the electron configuration.

In the case of an electron configuration, you first write down the orbital name, for example 1s, 2s or 2p. The number of electrons that were accommodated in these orbitals is noted as a superscript number. As we have already found out, the 1s orbital can be filled with a maximum of 2 electrons (with different spins).

So we write: 1s²

Alternatively, the following (detailed) notation is also used:

The opposite direction of the arrows shows the opposite spin of the electrons. So we have now occupied the 1s orbital with the maximum number of electrons. If we take a look at the periodic table of the elements, we can see that the element with 2 electrons is helium. So now we have already figured out the electron configuration of helium.

If we consider the next element in the periodic table with 3 electrons (lithium), we can also note the electron configuration for this. However, with lithium we already need another orbital, since the 1s orbital is completely filled.

The next orbital would be the 2s orbital, in which the next electron can be found:

In short, the electron configuration for the element lithium is: 1s² 2s & sup1

For the correct occupation of the existing orbitals with electrons, two important rules must be observed:

Hund's rule describes a very important principle in which orbitals are filled with electrons.

The system is precisely at its lowest energy level (and therefore also the most stable) when there are as many electrons as possible with parallel spins at the same energy level.

Let us consider the electron configuration of oxygen as an example of Hund’s rule. Here we find 8 electrons. Since the 2s orbital can only be occupied by 2 electrons, we also need the following orbital, which is the 2p orbital. A maximum of 6 electrons can be placed in p orbitals (see explanation above). If one were to disregard Hund’s rule, the electron configuration of oxygen would probably be noted as follows:

However, as already indicated, this electron configuration is wrong, since Hund’s rule was not observed here.

Correctly, one would have to consider with the electron configuration that with equivalent energy levels there must be as many electrons with parallel spin as possible. This means that you first fill an electron (with a parallel spin) into each orbital. Only then do you add the following electrons (with opposite spin).

The correct electron configuration for oxygen is therefore:

Instead of the 2 electrons with a parallel spin, we find 3 electrons with a parallel spin in this variant.

This variant must therefore be the correct one.

The following table is intended to clarify the occupation of the orbitals with electrons using the periodic table of the elements:

Now that we know how to name orbitals and how to fill them with electrons, we can now also describe the electron configuration for some elements. Let's use sodium as an example.

That sodium has 11 electrons. Since only 10 electrons together fit into the 1s, 2s and 2p orbital, the next orbital must also be filled. After a quick look at the table above, we know that this is the 3s orbital.

The electron configuration is:

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## Subjects of the natural sciences

The natural sciences deal with the study of the animate as well as the inanimate nature and can be subdivided into several sub-areas or subject areas:

the physics deals with matter and energy in time and space. the astronomy especially explores the celestial bodies from this point of view. the biology or the biosciences are responsible for living organisms and all factors of inanimate nature, insofar as they are of importance for living organisms. the chemistry deals with atoms and how they can be connected. The planet earth, with which the earth sciences deal with.

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## Hund's rules - chemistry and physics

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