Question

Which of the following about the electron orbital is false? (1) No orbital can contain more than two electrons. (2) If two electrons occupy the same orbital, they must have different spins. (3) No two orbitals in an atom can have the same energy. (4) The number of orbitals in different subshells is not the same.

Short answer

Statement (3) is false.

Step-by-step solution

Analyze Statement (1)

Consider whether no orbital can contain more than two electrons. The Pauli Exclusion Principle states that no two electrons in an atom can have the same set of quantum numbers, thus a single orbital can hold at most two electrons with opposite spins. Therefore, statement (1) is true.

Analyze Statement (2)

Consider whether two electrons in the same orbital must have different spins. According to the Pauli Exclusion Principle, if two electrons share the same orbital, they must indeed have opposite spins. Therefore, statement (2) is true.

Analyze Statement (3)

Consider whether no two orbitals in an atom can have the same energy. In reality, orbitals within the same subshell (e.g., the three 2p orbitals) have the same energy, known as being degenerate. Therefore, statement (3) is false.

Analyze Statement (4)

Consider whether the number of orbitals in different subshells is not the same. This is true as well; for instance, the s subshell has 1 orbital, the p subshell has 3 orbitals, the d subshell has 5 orbitals, and the f subshell has 7 orbitals. Therefore, statement (4) is true.

Key concepts

Pauli Exclusion Principle

The Pauli Exclusion Principle is a fundamental concept in quantum mechanics. It states that no two electrons in an atom can have the same set of quantum numbers.
This means that in any given orbital, which is defined by a set of quantum numbers, there can be at most two electrons, and they must have opposite spins.
To put it simply, an orbital can hold only two electrons, and these electrons must have different spin quantum numbers: one with spin-up (+1/2) and one with spin-down (-1/2).
This principle helps to explain the structure and behavior of atoms, playing a critical role in the arrangement of electrons in an atom's orbitals.

Electrons in Orbitals

Electrons are found in regions around the nucleus of an atom called orbitals. Each orbital has a specific shape and energy level.
Orbitals are described by four quantum numbers: the principal quantum number (n), the angular momentum quantum number (l), the magnetic quantum number (m_l), and the spin quantum number (m_s).
These quantum numbers help in categorizing the electrons' positions and their energies.
When filling these orbitals, electrons follow specific rules, including the Pauli Exclusion Principle and Hund's Rule, ensuring electrons are distributed in the most stable configuration.
The arrangement of electrons in various orbitals determines the chemical properties and reactivity of the atom.

Degenerate Orbitals

Degenerate orbitals are orbitals in the same subshell that have the same energy level. For example, the three 2p orbitals (2p_x, 2p_y, 2p_z) in an atom are degenerate, meaning they have identical energies.
This concept is essential in understanding how electron configurations work and how electrons fill available orbitals.
When electrons occupy degenerate orbitals, Hund's Rule states that electrons will fill each orbital singly before pairing up, to minimize electron-electron repulsion and thus lower the energy of the atom.
This is why you often see diagrams showing single electrons in each orbital of the same subshell before any orbitals are filled with two electrons.

Subshells and Orbitals

Orbital types are grouped into subshells, designated by the letters s, p, d, and f. Each subshell can contain a different number of orbitals.

• The s subshell has 1 orbital.
• The p subshell has 3 orbitals.
• The d subshell has 5 orbitals.
• The f subshell has 7 orbitals.

Each orbital in a given subshell has a specific orientation in space, and collectively, these orbitals describe the region in space where the probability of finding an electron is highest.
The number of orbitals in each subshell determines how many electrons the subshell can hold. For instance, the s subshell (with 1 orbital) can hold 2 electrons, while the p subshell (with 3 orbitals) can hold 6 electrons.
This arrangement of orbitals and subshells provides the framework for the electron configurations observed in atoms.