Quantum Numbers: Magnetic Quantum Number: Videos & Practice Problems

The magnetic quantum number ($m_l$) is crucial for understanding the orientation and location of electrons within an atom's orbitals. It arises from the angular momentum quantum number ($l$), indicating the shape and energy level of the orbital. The $m_l$ values range from $-l$ to $+l$, including all whole numbers in between, which correspond to the specific orbitals within a subshell. For instance, if $l$ is 2, $m_l$ can be $-2$, $-1$, $0$, $+1$, or $+2$. These values help to identify the orbital's numerical location, with s subshells having one orbital, p subshells three, d subshells five, and f subshells seven, leading to a maximum electron capacity of 2, 6, 10, and 14 respectively. This concept is foundational for understanding electron configurations and will be further explored when discussing the spin quantum number.

Orbitals Review

The magnetic quantum number is essential in understanding the behavior of electrons within an atom, particularly in relation to orbitals. An orbital is defined as the region within a subshell where a maximum of two specific electrons can be located. This concept is crucial as it provides insights into both the energy level of the electrons and the shape of the orbitals they occupy.

To comprehend the magnetic quantum number's role, it's important to recognize its relationship with the principal quantum number (n) and the azimuthal quantum number (l). The principal quantum number indicates the energy level of the electron, while the azimuthal quantum number defines the shape of the orbital. The magnetic quantum number, which can take on integer values ranging from -l to +l, specifies the orientation of the orbital in space.

For example, in a p subshell where l = 1, the magnetic quantum number can be -1, 0, or +1, corresponding to the three possible orientations of p orbitals (px, py, pz). Understanding these relationships is fundamental for predicting the arrangement of electrons in an atom and their subsequent chemical behavior.

Quantum Numbers and Orbitals Example

In the context of quantum mechanics and atomic structure, the principal quantum number (n) indicates the energy level of an electron in an atom. For the 4th principal level, n is equal to 4. The sublevel designation provides further detail about the shape and type of orbitals present. In this case, the f sublevel is specified, which corresponds to a set of orbitals characterized by their complex shapes and the ability to hold a maximum of 14 electrons.

Thus, when identifying the orbitals in the 4th principal level and f sublevel, we refer to the 4f orbitals. The notation indicates that these orbitals are part of the fourth energy level and belong to the f sublevel, confirming that the correct identification is indeed the 4f set of orbitals.

Magnetic Quantum Number

The magnetic quantum number, denoted as \( m_l \), describes the orientation of atomic orbitals and provides insight into the location of electrons within these orbitals. Each quantum number has specific limitations, and for \( m_l \), its values are determined by the angular momentum quantum number \( l \). The range of \( m_l \) extends from \(-l\) to \(+l\), including all integer values in between.

For instance, if \( l = 2 \), then \( m_l \) can take on the values of \(-2, -1, 0, +1, +2\). This relationship can be summarized as follows: when \( l = 0 \), \( m_l = 0 \); when \( l = 1 \), \( m_l \) ranges from \(-1\) to \(+1\); when \( l = 2\), it ranges from \(-2\) to \(+2\); and when \( l = 3\), it ranges from \(-3\) to \(+3\).

The subshell letters—s, p, d, and f—correspond to specific values of \( l \): \( l = 0 \) for s, \( l = 1 \) for p, \( l = 2 \) for d, and \( l = 3 \) for f. Knowing the subshell letter allows us to determine the associated \( l \) value, and consequently, the possible \( m_l \) values. For example, the s subshell has one spherical orbital (with \( m_l = 0 \)), while the p subshell has three orbitals corresponding to \( m_l = -1, 0, +1\).

In terms of electron capacity, each subshell can hold a maximum number of electrons: the s subshell can accommodate 2 electrons, the p subshell can hold 6, the d subshell can contain 10, and the f subshell can accommodate 14 electrons. This capacity is crucial for understanding electron configurations and will be further explored in relation to the spin quantum number.

Overall, the magnetic quantum number \( m_l \) is essential for determining the spatial orientation of orbitals and the distribution of electrons in an atom, which is foundational for understanding atomic structure and behavior.

Magnetic Quantum Example

In quantum mechanics, the magnetic quantum number, denoted as \( m_l \), is crucial for understanding the orientation of orbitals in an atom. The values of \( m_l \) are determined by the azimuthal quantum number \( l \), which corresponds to the type of subshell. For the f subshell, \( l \) is equal to 3. This means that the possible values for \( m_l \) range from \(-l\) to \(+l\), which translates to the values \(-3, -2, -1, 0, +1, +2, +3\) for the 7f set of orbitals.

Therefore, the valid magnetic quantum numbers for the 7f orbitals are \(-3, -2, -1, 0, +1, +2, +3\). Any value outside this range, such as \( +4 \), is not a valid magnetic quantum number for the f subshell. Thus, when identifying which number is not valid for the 7f orbitals, \( +4 \) is the correct answer, as it exceeds the allowable range for \( m_l \).

How many different values of m_l are possible for a 4d set of orbitals?

• A. 1
• B. 3
• C. 7
• D. 5
• E. 2

Answer: (D)

Select a correct set of values for an electron found within the designated 5d orbital.

• A. n = 5, l = 2, m_l = 0
• B. n = 5, l = 3, m_l = +1
• C. n = 5, l = 3, m_l = 0
• D. n = 5, l = 5, m_l = – 2
• E. n = 5, l = 2, m_l = +5

Answer: (A)

Which of the following statements is false?
a) A set of d orbitals contains 5 orbitals.
b) A set of 4s orbitals would have more energy than a set of 3p orbitals.
c) The second shell of an atom possesses d orbitals.
d) A set of f orbitals contains 3 orbitals.
e) The first energy level contains only s orbitals.

• A. a, b
• B. b, d
• C. c, d
• D. d, e
• E. b, e

Answer: (C)

Here’s what students ask on this topic:

How can I find the magnetic quantum number?

The magnetic quantum number, designated as $m_l$, can be found once you know the orbital angular momentum quantum number, or the azimuthal quantum number, denoted as $l$. For a given value of $l$, which can range from 0 to $n-1$ (where $n$ is the principal quantum number), $m_l$ can take on integer values ranging from $-l$ to $+l$, including zero.

So, if you have an electron in an orbital with $l=2$, the possible values for $m_l$ would be -2, -1, 0, 1, and 2. Each of these corresponds to a different orientation of the orbital in three-dimensional space. Remember that $l$ is related to the shape of the orbital (s, p, d, f corresponding to $l$ values of 0, 1, 2, 3, respectively), and $m_l$ relates to the orientation of that orbital.

What does the magnetic quantum number determine?

The magnetic quantum number, designated as $m_l$, is one of the four quantum numbers that describe the unique quantum state of an electron in an atom. It determines the orientation of the electron's orbital around the nucleus. Specifically, the magnetic quantum number can take on integer values ranging from $-l$ to $+l$, where $l$ is the azimuthal (or angular momentum) quantum number associated with the orbital shape.

For example, if an electron is in a p-orbital, where the azimuthal quantum number $l$ is 1, the magnetic quantum number $m_l$ can have values of $-1$, $0$, or $+1$, corresponding to the three different orientations that a p-orbital can have in space. These orientations are often depicted as the p_x, p_y, and p_z orbitals. The magnetic quantum number is particularly important when considering the effect of an external magnetic field on an electron, as it helps to determine the electron's energy in the presence of that field due to the Zeeman effect.

What is the magnetic quantum number?

The magnetic quantum number, symbolized as $m_l$, is one of four quantum numbers used in quantum mechanics to describe the unique quantum state of an electron. It specifically describes the orientation of an electron's orbital around a nucleus. The magnetic quantum number can take on integer values ranging from $-l$ to $+l$, where $l$ is the azimuthal quantum number or angular momentum quantum number associated with the electron's orbital.

For example, if an electron is in a p-orbital, the azimuthal quantum number $l$ is 1, and thus the magnetic quantum number $m_l$ can have values of $-1$, $0$, or $+1$. These values correspond to the different orientations an electron's orbital can have in a three-dimensional space, which becomes particularly relevant in the presence of a magnetic field, as it leads to the splitting of energy levels, a phenomenon known as Zeeman splitting. The magnetic quantum number helps in understanding the spatial distribution of electrons in an atom and is crucial for predicting the magnetic properties of an atom or molecule.

How can I find the magnetic quantum number?

The magnetic quantum number, designated as $m_l$, can be found once you know the orbital angular momentum quantum number, or the azimuthal quantum number, denoted as $l$. For a given value of $l$, which can range from 0 to $n-1$ (where $n$ is the principal quantum number), $m_l$ can take on integer values ranging from $-l$ to $+l$, including zero.

So, if you have an electron in an orbital with $l=2$, the possible values for $m_l$ would be -2, -1, 0, 1, and 2. Each of these corresponds to a different orientation of the orbital in three-dimensional space. Remember that $l$ is related to the shape of the orbital (s, p, d, f corresponding to $l$ values of 0, 1, 2, 3, respectively), and $m_l$ relates to the orientation of that orbital.