The Electron Configuration: Quantum Numbers: Videos & Practice Problems

Quantum Numbers and Electron Configuration Example

To determine the set of four quantum numbers for the sixth electron of an oxygen atom, we first need to understand the electron configuration of oxygen. With an atomic number of 6, the electron configuration is represented as 1s² 2s² 2p⁴. This indicates that oxygen has a total of six electrons distributed across its orbitals.

In the electron orbital diagram, we fill the orbitals according to the Aufbau principle, Pauli exclusion principle, and Hund's rule. The filling sequence starts with the 1s orbital, which can hold two electrons (1s²), followed by the 2s orbital (2s²), and then the 2p orbitals. For the 2p orbitals, we first half-fill each of the three available orbitals before pairing up the electrons, resulting in the configuration of 2p⁴ being filled as follows: up, up, up, down, down.

To identify the quantum numbers for the sixth electron, we note its position in the orbital diagram. The sixth electron is the last one added to the 2p orbitals. The relevant quantum numbers are defined as follows:

• Principal quantum number (n): This indicates the energy level of the electron. For the sixth electron in the 2p orbital, n = 2.
• Azimuthal quantum number (l): This describes the subshell of the electron. For a p orbital, l = 1.
• Magnetic quantum number (m_l): This specifies the orientation of the orbital. The sixth electron occupies the m_l = 0 orbital within the 2p subshell.
• Spin quantum number (m_s): This indicates the spin direction of the electron. Since the sixth electron is represented as pointing up, m_s = +1/2.

Thus, the complete set of quantum numbers for the sixth electron in an oxygen atom is:

n = 2, l = 1, m_l = 0, m_s = +1/2.

Understanding these quantum numbers is essential for grasping the behavior of electrons in atoms and their arrangement in various energy levels and subshells.

Give the set of four quantum numbers that represent the indicated electron in each of the following elements. 
Mg (7th electron) 

• A. n = 2; l = 2; ml = 0; ms = +1/2
• B. n = 2; l = 1; ml = 0; ms = -1/2
• C. n = 2; l = 1; ml = +1; ms = +1/2
• D. n = 2; l = 1; ml = +1; ms = -1/2
• E. n = 2; l = 1; ml = -1; ms = +1/2

Answer: (C)

Give the set of four quantum numbers that represent the indicated electron in each of the following elements. 
Cl^– (18th electron)

• A. n = 3; l = 0; ml = +1; ms = -1/2
• B. n = 3; l = 0; ml = -1; ms = -1/2
• C. n = 3; l = 2; ml = +1; ms = -1/2
• D. n = 3; l = 1; ml = +1; ms = +1/2
• E. n = 3; l = 1; ml = +1; ms = -1/2

Answer: (E)

Here's what students ask on this topic:

What are the four quantum numbers and what does each represent in electron configuration?

The four quantum numbers are essential for describing the unique state of an electron in an atom. The principal quantum number ($n$) indicates the energy level and size of the electron shell, with higher values meaning electrons are farther from the nucleus. The angular momentum quantum number ($l$) defines the shape of the orbital within a subshell, where $l\; =\; 0$ corresponds to s orbitals, $l\; =\; 1$ to p, $l\; =\; 2$ to d, and $l\; =\; 3$ to f orbitals. The magnetic quantum number ($\mathrm{m\_l}$) specifies the orientation of the orbital within the subshell, ranging from $-l$ to $+l$. Lastly, the spin quantum number ($\mathrm{m\_s}$) describes the electron's spin, which can be either $+\backslash (\backslash frac\{1\}\{2\}\backslash )$ (spin up) or $-\backslash (\backslash frac\{1\}\{2\}\backslash )$ (spin down). Together, these numbers uniquely identify an electron's position and energy in an atom.

How does the Aufbau principle determine the order of electron filling in orbitals?

The Aufbau principle guides the order in which electrons fill atomic orbitals, starting from the lowest energy level to higher ones. According to this principle, electrons first occupy the 1s orbital, then move to 2s, followed by 2p, 3s, 3p, and so on. This order is based on increasing energy levels and subshells. By following the Aufbau principle, we can number electrons sequentially as they fill orbitals, which helps in assigning the correct quantum numbers to each electron. This principle ensures that electrons occupy the most stable (lowest energy) configuration possible, which is fundamental for understanding electron configurations and predicting chemical behavior.

What is the significance of the magnetic quantum number ($m\_l$) in electron configuration?

The magnetic quantum number ($m\_l$) specifies the orientation of an orbital within a given subshell. For a subshell with angular momentum quantum number $l$, $m\_l$ can take integer values from $-l$ to $+l$. For example, in a d subshell where $l\; =\; 2$, $m\_l$ can be $-2,\; -1,\; 0,\; +1,\; +2$, representing the five different d orbitals. This quantum number helps distinguish orbitals that have the same shape and energy level but differ in spatial orientation. Understanding $m\_l$ is crucial for determining how electrons are distributed among orbitals within a subshell and for predicting magnetic properties of atoms.

How does the spin quantum number ($m\_s$) affect electron configuration and orbital occupancy?

The spin quantum number ($m\_s$) describes the intrinsic spin of an electron within an orbital, which can be either $+\backslash (\backslash frac\{1\}\{2\}\backslash )$ (spin up) or $-\backslash (\backslash frac\{1\}\{2\}\backslash )$ (spin down). Each orbital can hold a maximum of two electrons, and these electrons must have opposite spins according to the Pauli exclusion principle. This spin pairing is essential because it allows two electrons to occupy the same orbital without violating quantum mechanical rules. The spin quantum number thus plays a key role in determining the electron configuration and the magnetic properties of atoms, as unpaired electrons contribute to paramagnetism.

How do you assign quantum numbers to electrons in an electron configuration?

To assign quantum numbers to electrons, start by writing the electron configuration following the Aufbau principle, which orders orbitals by increasing energy. Number the electrons sequentially as they fill each orbital. For each electron, the principal quantum number ($n$) corresponds to the shell number (e.g., 1 for 1s, 2 for 2p). The angular momentum quantum number ($l$) is determined by the subshell type: 0 for s, 1 for p, 2 for d, and 3 for f. The magnetic quantum number ($m\_l$) ranges from $-l$ to $+l$ and identifies the specific orbital within the subshell. Finally, the spin quantum number ($m\_s$) is assigned as $+\backslash (\backslash frac\{1\}\{2\}\backslash )$ for the first electron in an orbital and $-\backslash (\backslash frac\{1\}\{2\}\backslash )$ for the second. This systematic approach ensures each electron's unique quantum state is accurately described.