Question

How many electrons may reside in a single orbital?

Short answer

A single orbital can hold a maximum of two electrons.

Step-by-step solution

Understand the Concept of an Orbital

An orbital is a region around the nucleus of an atom where an electron is likely to be found. According to quantum mechanics, each orbital has a specific energy level and a defined space where the probability of finding an electron is high.

Recognize the Pauli Exclusion Principle

The Pauli Exclusion Principle states that no two electrons within an atom can have the same set of quantum numbers. This principle implies a restriction on the number of electrons that can be accommodated in a single orbital.

Identify the Spin Quantum Number

Electrons have a property called spin, which can be either +1/2 or -1/2. In a single orbital, one electron can have a spin quantum number of +1/2 (spin up), while a second electron can have a spin quantum number of -1/2 (spin down).

Calculate the Maximum Number of Electrons in an Orbital

Following the Pauli Exclusion Principle and considering the possible spin states, each orbital can hold a maximum of two electrons, one with each type of spin.

Key concepts

Quantum Mechanics

Quantum mechanics is a fundamental theory in physics that describes the behavior of extremely small particles, like electrons in atoms. It introduces the concept of atomic orbitals, which are defined regions around an atom's nucleus where an electron is likely to be found. Instead of thinking of electrons as particles orbiting the nucleus in fixed paths, quantum mechanics describes them as being smeared out in these orbitals. This theory helps explain various properties of matter at the atomic level.

In quantum mechanics, each atomic orbital is associated with particular energy levels, which are quantized, meaning electrons can only occupy certain discrete energy levels. This quantization is a key idea that differentiates quantum mechanics from classical mechanics. By using wave functions, a probability distribution can be calculated for the location of an electron, enabling various phenomena to be understood, including chemical bonding and the structure of atoms.

Pauli Exclusion Principle

The Pauli Exclusion Principle is a crucial rule in quantum mechanics and atomic theory. Formulated by Wolfgang Pauli in 1925, it states that no two electrons in an atom can have the same set of quantum numbers. Quantum numbers are sets of values that describe specific properties of electrons, like their energy levels, sub-levels, and orientation.

• Each electron in an atom is described by a unique combination of four quantum numbers: principal, azimuthal, magnetic, and spin quantum numbers.
• The Pauli Exclusion Principle essentially limits the number of electrons that can occupy a single orbital to two.
• This principle explains why atoms have distinct electron configurations and how electrons fill atomic orbitals in a specific sequence.

Without the Pauli Exclusion Principle, atoms would not have the unique structure they do today, leading to vastly different chemical behaviors.

Spin Quantum Number

The spin quantum number is one of the four quantum numbers used to describe the properties of electrons in atoms. It refers to the intrinsic spin of an electron, which is an inherent form of angular momentum.

• The spin quantum number can have one of two possible values: +1/2 or -1/2.
• These values indicate the direction of the electron's spin, commonly referred to as "spin up" (+1/2) or "spin down" (-1/2).
• This quantum property of electrons is crucial in defining the way electrons fill orbitals.

Due to the spin quantum number, only two electrons can occupy the same orbital, each having opposite spins. This principle ensures that electrons maintain unique quantum states within an atom, adhering to the Pauli Exclusion Principle. Spin plays a significant role in chemistry and solid-state physics, influencing phenomena like magnetism and the formation of chemical bonds.