A Closer Look at Shells, Subshells, and also OrbitalsSubshellsProblems

A complete of 4 quantum number are offered to describe completely the movement and trajectories of every electron in ~ an atom. The mix of all quantum numbers of all electrons in an atom is described by a wave role that complies with the Schrödinger equation. Every electron in an atom has actually a unique set of quantum numbers; follow to the Pauli exemption Principle, no two electrons have the right to share the same combination of four quantum numbers. Quantum numbers room important because they can be offered to recognize the electron construction of an atom and the probable location of the atom"s electrons. Quantum numbers are additionally used to know other attributes of atoms, such together ionization energy and also the atom radius.

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In atoms, there room a total of four quantum numbers: the principal quantum number (n), the orbital angular inert quantum number (l), the magnetic quantum number (ml), and the electron rotate quantum number (ms). The principal quantum number, (n), explains the energy of one electron and also the many probable street of the electron native the nucleus. In other words, it refers to the size of the orbital and the power level one electron is inserted in. The number of subshells, or (l), defines the shape of the orbital. That can likewise be used to recognize the number of angular nodes. The magnetic quantum number, ml, describes the energy levels in a subshell, and ms describes the spin on the electron, which have the right to either it is in up or down.

The primary Quantum Number ((n))

The principal quantum number, (n), designates the primary electron shell. Because n defines the many probable distance of the electrons from the nucleus, the bigger the number n is, the farther the electron is indigenous the nucleus, the bigger the dimension of the orbital, and also the larger the atom is. n deserve to be any kind of positive integer starting at 1, together (n=1) designates the an initial principal covering (the innermost shell). The first principal shell is likewise called the floor state, or lowest energy state. This explains why (n) deserve to not it is in 0 or any negative integer, since there exists no atoms v zero or a an unfavorable amount of energy levels/principal shells. When an electron is in an excited state or that gains energy, it might jump to the second principle shell, where (n=2). This is referred to as absorption because the electron is "absorbing" photons, or energy. Known as emission, electrons can also "emit" power as they run to lower principle shells, where n to reduce by entirety numbers. As the power of the electron increases, therefore does the major quantum number, e.g., n = 3 suggests the third principal shell, n = 4 suggests the 4th principal shell, and so on.

Example (PageIndex1)

If n = 7, what is the principal electron shell?

Example (PageIndex2)

If an electron jumped from power level n = 5 to power level n = 3, did absorption or emissions of a photon occur?


Emission, due to the fact that energy is lost by relax of a photon.

The orbital Angular inert Quantum Number ((l))

The orbit angular inert quantum number (l) determines the form of an orbital, and therefore the angular distribution. The variety of angular nodes is equal to the worth of the angular momentum quantum number (l). (For much more information about angular nodes, see electronic Orbitals.) Each worth of (l) shows a details s, p, d, f subshell (each distinctive in shape.) The worth of (l) is dependent on the principal quantum number (n). Uneven (n), the worth of (l) have the right to be zero. That can additionally be a positive integer, however it cannot be bigger than one much less than the major quantum number ((n-1)):

Example (PageIndex3)

If (n = 7), what room the possible values that (l)?


Since (l) have the right to be zero or a positive integer less than ((n-1)), it deserve to have a worth of 0, 1, 2, 3, 4, 5 or 6.

Example (PageIndex4)

If (l = 4), how plenty of angular nodes go the atom have?


The number of angular nodes is equal to the value of l, therefore the variety of nodes is also 4.

The Magnetic Quantum Number ((m_l))

The magnetic quantum number (m_l) identify the variety of orbitals and also their orientation in ~ a subshell. Consequently, that value depends on the orbital angular momentum quantum number (l). Given a particular (l), (m_l) is an interval ranging from (–l) to (+l), therefore it have the right to be zero, a an adverse integer, or a hopeful integer.

Example (PageIndex5)

Example: If (n=3), and also (l=2), climate what are the possible values the (m_l)?


Since (m_l) must selection from (–l) to (+l), then (m_l) deserve to be: -2, -1, 0, 1, or 2.

The Electron turn Quantum Number ((m_s))

Unlike (n), (l), and (m_l), the electron spin quantum number (m_s) does not count on an additional quantum number. That designates the direction the the electron spin and may have a spin of +1/2, represented by↑, or –1/2, represented by ↓. This way that as soon as (m_s) is confident the electron has actually an upward spin, which have the right to be described as "spin up." as soon as it is negative, the electron has a bottom spin, so the is "spin down." The significance of the electron spin quantum number is its determination of one atom"s capacity to create a magnetic field or not. (Electron Spin.)

Example (PageIndex5)

List the possible combinations the all four quantum numbers once (n=2), (l=1), and also (m_l=0).


The fourth quantum number is live independence of the very first three, enabling the very first three quantum numbers of 2 electrons to be the same. Since the spin can be +1/2 or =1/2, there are two combinations:

(n=2), (l=1), (m_l =0), (m_s=+1/2) (n=2), (l=1), (m_l=0), (m_s=-1/2)

Example (PageIndex6)

Can one electron with (m_s=1/2) have actually a bottom spin?


No, if the worth of (m_s) is positive, the electron is "spin up."

A Closer Look in ~ Shells, Subshells, and also Orbitals

Principal Shells

The worth of the primary quantum number n is the level the the principal digital shell (principal level). All orbitals that have actually the very same n value are in the same principal level. For example, all orbitals top top the 2nd principal level have actually a principal quantum variety of n=2. Once the worth of n is higher, the variety of principal electronic shells is greater. This reasons a higher distance between the the furthest electron and also the nucleus. As a result, the size of the atom and its atomic radius increases.


Because the atomic radius increases, the electrons room farther native the nucleus. For this reason it is much easier for the atom to expel one electron due to the fact that the nucleus walk not have as strong a pull on it, and the ionization power decreases.


The number of values of the orbital angular number l can likewise be offered to identify the variety of subshells in a principal electron shell:

when n = 1, l= 0 (l take away on one value and thus there have the right to only it is in one subshell) once n = 2, l= 0, 1 (l bring away on two values and also thus there room two possible subshells) when n = 3, l= 0, 1, 2 (l take away on three values and also thus there room three feasible subshells)

After looking in ~ the examples above, we watch that the value of n is same to the number of subshells in a principal digital shell:

principal shell v n = 1 has one subshell primary shell v n = 2 has two subshells major shell v n = 3 has three subshells

To recognize what type of feasible subshells n has, these subshells have been assigned letter names. The worth of l identify the name of the subshell:

surname of Subshell value of (l)
s subshell 0
p subshell 1
d subshell 2
f subshell 3


principal shell v n = 1 has one s subshell (l = 0) major shell v n = 2 has one s subshell and one p subshell (l = 0, 1) primary shell v n = 3 has actually one s subshell, one ns subshell, and also one d subshell (l = 0, 1, 2)

We deserve to designate a principal quantum number, n, and a specific subshell by combining the worth of n and also the name of the subshell (which can be discovered using l). Because that example, 3p describes the 3rd principal quantum number (n=3) and the ns subshell (l=1).

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The variety of orbitals in a subshell is equivalent to the variety of values the magnetic quantum number ml take away on. A helpful equation to determine the number of orbitals in a subshell is 2l +1. This equation will not offer you the value of ml, yet the number of possible worths that ml have the right to take ~ above in a particular orbital. For example, if l=1 and ml deserve to have values -1, 0, or +1, the value of 2l+1 will be three and also there will certainly be three various orbitals. The name of the orbitals are called after the subshells lock are uncovered in:

s orbitalsp orbitalsd orbitalsf orbitals
l 0 1 2 3
ml 0 -1, 0, +1 -2, -1, 0, +1, +2 -3, -2, -1, 0, +1, +2, +3
Number the orbitals in designated subshell 1 3 5 7

In the number below, we see examples of 2 orbitals: the ns orbital (blue) and also the s orbital (red). The red s orbit is a 1s orbital. To photo a 2s orbital, imagine a layer comparable to a cross ar of a jawbreaker around the circle. The class are depicting the atoms angular nodes. To photo a 3s orbital, imagine one more layer about the circle, and so on and so on. The p orbital is comparable to the form of a dumbbell, through its orientation in ~ a subshell relying on ml. The shape and also orientation of one orbital relies on l and ml.


To visualize and organize the an initial three quantum numbers, we can think that them as constituents the a house. In the following image, the roof represents the principal quantum number n, every level to represent a subshell l, and each room to represent the various orbitals ml in every subshell. The s orbital, because the value of ml have the right to only be 0, deserve to only exist in one plane. The p orbital, however, has actually three feasible values the ml and also so it has three feasible orientations the the orbitals, presented by Px, Py, and also Pz. The sample continues, v the d orbit containing 5 feasible orbital orientations, and also f has actually 7:

Principle Quantum Number 4.jpgwhat are the possible values of n and ml for an electron in a 5 p orbital?