# Schrödinger's atomic model, SPDF notation

This is part of preliminary HSC Chemistry course under the topic of Atomic Structure and Atomic Mass

### HSC Chemistry Syllabus

• Model the atom's discrete energy levels, including electronic configuration and SPDF notation (ACSCH017, ACSCH018, ACSCH020, ACSCH021)
• Investigate energy levels in atoms and ions through:
• Examining spectral evidence for the Bohr model and introducing the Schrödinger model

### Schrödinger Quantum Mechanical Model

In 1926, Erwin Schrödinger proposed a model to elucidate the behavior of electrons in an atom. Instead of tracing a precise path of electrons around the nucleus, he applied mathematical equations to predict the probability of finding an electron in a particular space. This approach, known as the quantum mechanical model, represents the atom as a nucleus enveloped by an electron cloud. ### Electron Orbitals

Electrons orbit the nucleus, which consists of protons and neutrons. As the energy of an electron increases, so does the size of its orbit. Schrödinger's model provides a probabilistic description of the electron's location around the nucleus. Due to the dual wave-particle nature of electrons, upon energy absorption, they shift to different energy levels, altering their orbital shapes. These paths, known as orbitals can assume varied forms - from the simplest spherical to the more complex dumbbell shapes and beyond.

### SPDF Electron Configuration

The arrangement of electrons within an atom's orbitals is called the electron configuration. The Schrödinger model accommodates this concept, with the most stable configuration termed the ground-state electron configuration - where all electrons reside in the lowest energy orbitals possible. Given that each orbital can hold a maximum of two electrons, we can predict the electron configurations of elements using the periodic table.

### Shells and Subshells

Electrons exist in shells denoted by the principal quantum number (n = 1, 2, 3, etc.). Each shell, barring the first one, contains several sub shells or energy sub levels. An electron's location is described by its shell (n) and a specific sub shell (s, p, d, f), within which it occupies an orbital.

In accordance with Pauli's Exclusion Principle, an orbital can hold a maximum of two electrons, each with opposite spin. Pauli's Exclusion Principle is discussed below.

Subshells, labelled as s, p, d, f, and so on, contain the orbitals that accommodate the electrons. These subshells differ in shape and energy level.

• The s sub-shell, the lowest energy level, contains one s-orbital and can accomodate two electrons.
• The p sub-shell, the next energy level, contains three p-orbitals (p_x, p_y, and p_z), each oriented differently at right angles to each other. This sub-shell can accomodate six electrons.
• The d sub-shell, the third energy level, contains five d-orbitals, and can accommodate ten electrons. The d-orbitals have complex shapes.
• The f sub-shell, the fourth energy level, contains seven f-orbitals, and can accomodate fourteen electrons. The f-orbitals, too, have complex shapes.

Below is a table describing the relationship between the principal quantum number of a shell and the numbers of sub-shells, orbitals and electrons

 Principal quantum number (n) Number of sub-shells (n) Types of sub-shells Number of orbitals in each sub-shell Maximum # electrons in each sub-shell Maximum # electrons in the shell 1 1 S 1 2 2 2 2 S P 1 3 2 6 8 3 3 S P D 1 3 5 2 6 10 18 4 4 S P D F 1 3 5 7 2 6 10 14 32

The diagram presented is known as an orbital diagram, a tool that facilitates the modeling and visualization of the spatial distribution of orbitals within a certain electron configuration. Starting from the bottom, the level marked '1' represents the lowest energy state.

Each horizontal line, denoted as '_', signifies an orbital. As we can observe, there's one orbital in the 's' subshell, three in the 'p' subshell, and so forth. Owing to the Pauli Exclusion Principle, each orbital can accommodate a maximum of two electrons. Hence, the electron capacity of each energy level increases progressively: the first level can hold two electrons, the second level can accommodate eight, the third level has room for eighteen, and so on. This ascending pattern continues in accordance with the increasing number of orbitals and subshells in each subsequent energy level SPDF Electron Configuration

The SPDF electron configuration provides a systematic method for noting the positions of all the electrons in an atom. The arrangement of electrons in an atom's orbitals is subject to three guiding principles:

1. Aufbau Principle

• Electrons fill the available orbitals starting from the lowest energy level.
• All orbitals within a particular energy level possess the same energy. For instance, the three 2p orbitals are equivalent in terms of energy.
2. Hund's Rule

• For orbitals of the same energy, electrons fill each orbital singly before any orbital gets a second electron.
• Electrons preferentially occupy individual orbitals rather than sharing orbitals.
3. Pauli Exclusion Principle

• Any given orbital can accommodate a maximum of two electrons, and these electrons must have opposite spins.
• The concept of 'spin' refers to an inherent property of electrons, which can be either 'up' or 'down Utilising the three rules governing electron configuration diagrams and our understanding of orbitals as probable paths for electrons, we can ascertain the orbitals where the electrons of particular elements are likely to reside.

In atoms with a neutral charge, the number of electrons is equal to the number of protons. As electrons fill the orbitals, they occupy the lowest energy orbitals first before progressing to higher energy levels.

Consider hydrogen, with an atomic number of 1. Its solitary electron must occupy the lowest energy orbital, which is the 1s orbital. Therefore, its electron configuration is written as 1s^1. Similarly, helium, with two protons, has an electron configuration of 1s^2. Lithium, with three protons, has an electron configuration of 1s^22s^1. This sequence follows the arrangement of s, p, d, and f orbitals in the periodic table. Consequently, boron, with an atomic number of 5, has an electron configuration of 1s^22s^22p^1.

Electron configuration can be represented as an orbital diagram, which illustrates the diverse orientations and spins of each electron. The diagram uses boxes or lines to denote the number of subshells (three for p-orbitals, five for d-orbitals, and seven for f-orbitals). Each box indicates an electron's spin, represented by arrows: up arrows for a spin of +½ and down arrows for -½.

For instance, hydrogen, with an electron configuration of 1s1, would be depicted as a single line with an upward arrow, representing the lone electron in the 1s orbital.

H: 1s

For helium, which has two protons and an electron configuration of 1s2, the orbital diagram would have an upward arrow and a downward arrow, representing two electrons with opposite spins.

He: 1s

For lithium, which has three protons and an electron configuration of 1s2 2s1, the diagram would be:

Li: 1s 2s

For carbon, with an electron configuration of 1s22s22p2, the orbital diagram would be:

C: 1s 2s ↑↑  2p

Here, the two upward arrows in the 2p subshell depict the two electrons in the 2p orbitals, both having the same spin as per Hund's rule. The arrow is an indication of the order of which orbitals should be filled: 1s, 2s, 2p, 3s, 3p, 3d, 4p, 5p, 6s, 4f, 5d, 6p, 7s, 5f, 6d, 7p

### Stability

Atoms achieve stability by adjusting their energy levels, often accomplished by gaining or losing electrons to complete their s and p subshells. The ultimate objective for all atoms is to attain a filled s and p subshell, which corresponds to the electron configuration of noble gases. This s^2p^6 configuration results in lowered energy and enhanced stability, providing the atoms with a 'noble gas-like' state. Noble gases are inherently stable, neither needing to lose nor gain electrons due to their full s and p subshells.

Drawing the Bohr model of an atom with the

s^2p^6 configuration reveals eight valence electrons in the outermost shell, a principle known as the octet rule. This rule asserts that atoms strive to have a total of eight valence electrons in their outermost shell.

Let's consider a few examples:

Sodium (Na)

• Initial configuration: 1s^22s^22p^63s^1 - unstable
• Target configuration (Neon, Ne): 1s^22s^22p^6 - stable

To achieve stability, sodium needs to lose its outer electron, transforming into a sodium ion (Na^+):

• Na^+ configuration: 1s^22s^22p^6 - stable

Chlorine (Cl)

• Initial configuration: 1s^22s^22p^63s^23p^5 - unstable
• Target configuration (Argon, Ar): 1s^22s^22p^63s^23p^6 - stable

To attain stability, chlorine aims to gain one electron, adopting an electron configuration similar to Argon:

• Cl^- configuration: 1s2^2s^22p^63s^23p^6 - stable"