Electron orbital

• The arrangement of electrons in shells and orbitals around the nucleus of an atom is governed by the Pauli exclusion principle. The Pauli exclusion principle applies to electrons, protons, neutrons, (and neutrinos). It ensures that no two electrons can occupy the same quantum state simultaneously, leading to the formation of distinct shells and sublevels within each shell, known as orbitals.
• The Pauli exclusion principle states that within an atom, each electron occupies a unique quantum state defined by its four quantum numbers: the principal quantum number (n), the azimuthal quantum number (l), the magnetic quantum number (m_l), and the spin quantum number (s).
• The four quantum numbers that together describe the quantum state of an electron govern its specific orbital position. These numbers are:
  • Principal quantum number (n): This quantum number determines the main energy level of the electron and, consequently, the distance from the nucleus. Higher values of n correspond to larger orbitals and higher energy levels.
  • Azimuthal quantum number (l): This quantum number determines the shape of the orbital. Different values of (l) correspond to different orbital shapes, such as s orbitals (l = 0), p orbitals (l= 1), d orbitals (l = 2), and so on.
  • Magnetic quantum number (m): This quantum number determines the orientation of the orbital in space. Different values of ml correspond to different orientations of the orbital relative to a magnetic field.
  • Spin quantum number (s): This quantum number determines the electron’s spin, which can be either +1/2 or -1/2. Two electrons in the same orbital can have opposite spins, satisfying the Pauli exclusion principle.

Shell	Orbital	Principal quantum number (n)	Azimuthal quantum number (ℓ)	Magnetic quantum number (mℓ)	Spin quantum number (s)
1	s	1	0	0	+1/2 or -1/2
2	s	2	0	0	+1/2 or -1/2
2	p	2	1	-1, 0, +1	+1/2 or -1/2
3	s	3	0	0	+1/2 or -1/2
3	p	3	1	-1, 0, +1	+1/2 or -1/2
3	d	3	2	-2, -1, 0, +1, +2	+1/2 or -1/2

This table shows the first few electron orbitals and their quantum numbers.

• The nucleus of an atom is positively charged. The amount of charge is determined by the number of protons in the nucleus. The greater the number of protons in an atom, the stronger the positive charge, and the stronger the force experienced by an electron.
• The electrostatic force, which governs the attraction between positively charged protons and negatively charged electrons in an atom, is directly proportional to the product of the charges between them.
• However, counterintuitively, as the number of protons (and thus the positive charge of the nucleus) increases, the average distance between the nucleus and its electrons (atomic radius) generally decreases. This is because the stronger nuclear pull outweighs the repulsion between electrons, causing them to occupy smaller orbitals closer to the nucleus.
• The characteristics of orbiting electrons, such as their energy levels and spatial distribution, are influenced by the strength of the electrostatic force exerted by the nucleus. The stronger the force, the more tightly bound the electrons are to the nucleus, and the lower their energy levels.

Fundamentals of Electron Orbitals

• • Quantization: Electron orbitals are quantized, meaning they have discrete energy levels and shapes. Electrons cannot exist between these levels or have intermediate shapes.
  • Pauli Exclusion Principle: No two electrons can occupy the same quantum state simultaneously. This principle ensures that each orbital can only hold a maximum of two electrons with opposite spins.
  • Aufbau Principle: Electrons fill orbitals in order of increasing energy, starting with the lowest energy orbitals and then filling higher energy orbitals as more electrons are added.
  • Electron Cloud: Electrons are not confined to specific points in space but rather occupy regions of probability. The electron cloud represents the probability of finding an electron in a particular region around the nucleus.
  • The arrangement of electrons in the electron orbitals of an atom is called the electron configuration of the atom. The electron configuration of an atom determines its chemical properties.

Electron velocity

• An electron’s velocity is primarily determined by its kinetic energy, which is the energy of motion. Kinetic energy is directly related to the electron’s speed, and the higher the kinetic energy, the faster the electron will be moving.
• There are several mechanisms by which electrons can gain kinetic energy and thus increase their velocity:
  • Absorption of energy: When an electron absorbs energy, such as from a photon of light, it can transition to a higher energy level and gain kinetic energy. This absorbed energy increases the electron’s speed and velocity.
  • Thermal excitation: In heated substances, atoms gain kinetic energy, causing their electrons to move more rapidly. This increase in kinetic energy corresponds to an increase in the average velocity of the electrons.
  • Electrical fields: Electric fields can accelerate or decelerate electrons depending on the direction of the field. Electrons moving in the direction of an electric field will gain kinetic energy and increase their velocity, while electrons moving against the field will lose kinetic energy and slow down.
  • Collisions: When electrons collide with other particles, such as atoms or other electrons, they can exchange energy. If the collision results in a transfer of kinetic energy to the electron, its velocity will increase.
• The velocity of an electron can affect the distribution of an electron within its orbital. When an electron has a higher velocity, it is more likely to be found further away from the nucleus, even within the same orbital. This is because the electron has more kinetic energy, which makes it less likely to be attracted to the positively charged nucleus.