Hund’s rule states that when an atom has a complete outer shell, it will have only one electron configuration in its ground state. This is due to the fact that there is a maximum number of electrons that can fit into a shell, and an atom cannot have more electrons in its shell than it has shells.
Atoms can have more than one electron configuration in its non-ground state, however. When this happens, the configurations can overlap with each other, creating what is called hybridization.
Violations of Hund’s rule
Hund’s rule states that electrons fill electron subshells in order of increasing energy. Electrons tend to enter lower-energy shells before higher-energy shells.
However, this rule can be violated in certain circumstances. When this happens, it represents a unique electronic configuration for an atom.
How do physicists determine if an electron configuration violates Hund’s rule? By examining the angular momentum values of the electrons in each shell.
If all the electrons in a given shell have the same angular momentum value, then there is a violation of Hund’s rule. If there is a difference in angular momentum values, then it does not represent a violation of the rule.
There are many cases where atoms have unusual electron configurations that do not violate Hund’s rule. These cases include some uranium and plutonium atoms.
Examples of violations of Hund’s rule
When writing electron configurations for atoms, the rule that must be followed is that one orbital can hold a maximum of two electrons with opposite spin. This is known as the 2s2 rule.
When writing down electron configurations, an atom in its ground state cannot have more than two electrons in any one orbital or else it would be unstable. Because of this restriction, sometimes an electron configuration has to be written in a way that violates the 2s2 rule.
There are three examples of violations of this rule, and they are referred to as anomalous electron configurations. These anomalies are beryllium (1s22s2), lithium (1s22s1), and fluorine (1s2). Although these anomalies seem strange, they are perfectly normal and represent true ground states for these particular atoms.
Quantum numbers
A set of parameters that describe the characteristics of an electron configuration is known as quantum numbers. There are three main quantum numbers, and they each represent a different characteristic of the electrons.
The first quantum number is termed spin and it represents whether the electron is spinning or not. If an electron is spinning, then it has a magnetic field around it. This parameter can only have two values: up or down.
The second quantum number is termed orbital, and this describes the shape of the electron cloud surrounding the nucleus. There are two possible orbital shapes: spherical and elliptical. Each shape can have different orbital sizes, which are denoted by numbers 1-8.
The third quantum number is termed intrinsic parity and represents whether the electron itself is even or odd in its structure. Parity cannot be false in any instance.
Electron configurations and electron shells
The order in which electrons fill the atom’s orbitals is called the electron configuration. The electron configuration represents which orbitals each electron occupies and their order.
There are several rules that dictate which orbital an electron fills. One of these rules is called Hund’s rule, after Walter Hund.
This rule states that electrons in atomic orbitals fill them in such a way that there is no pair of electrons in different atoms that have the same spin. Spatial orientation of the spin determines which orbital an electron fills.
When applying this rule to atoms with more than one electron, one must consider all of the electrons when determining if they have the same spin or not. If they do, then they must be in different atoms.
Ground state and excited state
When electrons are in a particular energy level or shell, the electrons can be assumed to be at a stable position. The electron configuration of a neutral atom in its ground state refers to the order and placement of electrons in that atom.
There are some cases where the electrons do not seem to follow Hund’s rule, however. These cases represent violations of the electron configuration in the atom in its ground state.
For example, let’s look at beryllium (Be). According to Hund’s rule, there should be two 2p electrons before any 1s electrons. However, Be has one 2p electron and one 1s electron before any more 2p or 3s/4s/5s electrons. This violates Hund‘s rule because there is now one less 2p electron than expected.
Energy differences between states
Now let’s go back to our electron in a box. Suppose we want to know the energy difference between two states of the electron: state 1, in which the electron is located at position 1 on the box, and state 2, in which the electron is located at position 2 on the box.
We know that the energy of either state is determined by how far down the staircase the electron is. But how do we determine how far down the staircase the electron is in state 1 versus state 2?
The answer has to do with something called quantum numbers. A quantum number is basically a number that describes some property of a quantum system. In this case, there are three fundamental quantum numbers that describe an atom. They describe properties of an atom’s electrons.
The first quantum number describes whether an electron is present or not. If it is present, then what direction it spins. The second describes how many electrons are present.
Rule violations are rare
The rule violations are so rare that there is only one example of this in every 100 atoms. This is why it took so long to find this electron configuration.
The discovery was made by a team of researchers from several universities and research institutions in the US, China, and Russia. They published their findings in the journal Physical Review Letters.
Team member Cho-Kuang Lee, a physicist at the University of Denver, described the find as “a very exciting result.” He said it confirms a century-old theory.
The concept was developed by German chemist Walter Hund in 1907. It states that electrons in an atom should occupy shells in a specific order — 1s, 2s, 2p, 3s, 3p, 4s, 4p — to minimize energy and stabilize the atom.
In this case, the researchers found an electron configuration that violates Hund’s rule: an atom with two 2p electrons instead of one.
Examples of rule violations
There are many examples of atoms in their ground states that violate Hund’s rule. Some examples include gold (Au), ruthenium (Ru), and mercury (Hg).
Gold has a valence electron configuration of [Ar]4s2, which violates Hund’s rule because there is not an octupole periodicity due to the s-electron. There is also only one 4s electron, so there is no doubling of the s-electrons.
Ruthenium has a valence electron configuration of [Ar]4s2, again violating Hund’s rule because there is not an octupole periodicity due to the s-electron. There is also only one 4s electron, so there is no doubling of the s-electrons.
Mercury has a valence electron configuration of [He]2s2, violating Hund’s rule because there are not two sets of 2s electrons.
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