Quantum numbers in Chemistry, are the sets of numbers that describe an electron's orbit and movement within an atom. When the quantum numbers of all the electrons in a given atom are added together, they must satisfy the Schrodinger equation.
Quantum numbers are the set of numbers used to describe the position and energy of an electron in an atom. There are four types of quantum numbers: principal, azimuthal, magnetic, and spin. Quantum numbers represent the values of a quantum system's conserved quantities.
Let's learn about all the quantum numbers in detail in this article.
What are Quantum Numbers?
Quantum numbers are the set of constant values in the quantum approach. Quantum Numbers or Electronic quantum numbers describe an electron with numerical values that provide solutions to the Schrodinger wave equation for hydrogen atoms these numbers can define the position, energy and orientation of an electron in an atom through the set of numbers.
According to the Pauli exclusion principle, no two electrons in an atom may have the same set of quantum numbers. A half-integer or integer value is used to characterize each quantum number. The principal, azimuthal and magnetic quantum numbers are respectively related to the size, shape, and orientation of the atom.
Four quantum numbers can be used to fully describe all of the properties of a given electron in an atom; these are:
- Principal quantum number
- Orbital angular momentum quantum number (or Azimuthal quantum number).
- Magnetic quantum number
- The electron spin quantum number
Types of Quantum Numbers
Four quantum numbers are used to fully describe all the characteristics of an electron in an atom. These quantum numbers are:
- Principal Quantum Number (n)
- Azimuthal Quantum Number (l)
- Magnetic Quantum Number (ml)
- Electron Spin Quantum Number (s)
Principal Quantum Number (n)
The symbol 'n' represents the principal quantum numbers. They denote the atom's primary electron shell. Because it describes the most likely distance between the nucleus and the electrons, a larger value of the principal quantum number implies a greater distance between the electron and the nucleus (which, in turn, implies a greater atomic size).
- The principal quantum number's value can be any integer with a positive value equal to or greater than one. The value n=1 denotes an atom's innermost electron shell, which corresponds to an electron's lowest energy state (or ground state).
- As a result, the principal quantum number, n, cannot have a negative value or be equal to zero because an atom cannot have a negative value or no value for a principal shell.
- When an electron is infused with energy (excited state), the electron jumps from one principal shell to a higher shell, causing the value of n to increase.
- Similarly, as electrons lose energy, they return to lower shells, lowering the value of n. Absorption refers to the increase in the value of n for an electron, emphasizing the photons or energy absorbed by the electron.
- Similarly, a decrease in the value of n for an electron is referred to as emission, and this is where the electrons emit their energy.
Azimuthal Quantum Number (l) - Orbital Angular Momentum Quantum Number
The azimuthal quantum number (or orbital angular momentum) describes the shape of an orbital. It is represented by the letter 'l,' and its value equals the total number of angular nodes in the orbital.
- A value of the azimuthal quantum number can denote either an s, p, d, or f subshell, the shapes of which vary.
- This value is determined by (and limited by) the value of the principal quantum number, i.e. the azimuthal quantum number ranges between 0 and (n-1).
- For example, if n = 3, the azimuthal quantum number can have three values: 0, 1, and 2.
- When l is set to zero, the resulting subshell is an 's' subshell.
- When l=1 and l=2, the resulting subshells are 'p' and 'd' subshells, respectively (respectively).
- As a result, when n=3, the three subshells that can exist are 3s, 3p, and 3d. In another case where n = 5, the possible values of l are 0, 1, 2, 3, and 4. If l = 3, the atom contains three angular nodes.
Magnetic Quantum Number (ml)
The magnetic quantum number determines the total number of orbitals in a subshell as well as their orientation. It is represented by the symbol 'ml.' This number represents the projection of the orbital's angular momentum along a given axis.
- The magnetic quantum number is determined by the azimuthal (or orbital angular momentum) quantum number.
- For a given value of l, the value of ml falls between -l to +l. As a result, it is indirectly dependent on the value of n.
- For example, if n = 4 and l = 3 in an atom, the magnetic quantum number can be -3, -2, -1, 0, +1, +2, and +3. The total number of orbitals in a given subshell is determined by the orbital's 'l' value.
- It is calculated using the formula (2l + 1). The '3d' subshell (n=3, l=2), for example, has 5 orbitals (2*2 + 1). Each orbital can hold two electrons. As a result, the 3d subshell can accommodate a total of 10 electrons.
Electron Spin Quantum Number (s)
The electron spin quantum number is independent of n, l, and ml values. The value of this number, denoted by the symbol ms, indicates the direction in which the electron is spinning.
- The ms value indicates the direction in which the electron is spinning. The electron spin quantum number can have values between +1/2 and -1/2.
- A positive value of ms denotes an upward spin on the electron, also known as spin up.
- If ms is negative, the electron in question is said to have a downward spin or spin down.
- The value of the electron spin quantum number determines whether or not the atom in question can generate a magnetic field. The value of ms can be generalized to ±½.
Significance of Quantum Numbers
Quantum numbers are significant because they can be used to estimate an atom's electron configuration and where its electrons are most likely to be located. The atomic radius and ionization energy of atoms, among other properties, is also determined by quantum numbers.
Each Quantum Number has its own significance which is describe in the following table:
Number | Symbol | Possible Values | Significance |
|---|
Principal Quantum Number | n | 1, 2, 3, 4, 5,..... | It describes the electron levels of an atom. |
|---|
Azimuthal Quantum Number | l | 0, 1, 2, 3,.... (n-1) | It represents the shape of the electron cloud. |
|---|
Magnetic Quantum Number | ml | -l,...., -1, 0, 1,...., l | It explains the orientation of the electron cloud. |
|---|
Spin Quantum Number | s | +1/2,-1/2 | It tells the spin electrons can have. |
|---|
Atomic Orbital
As we know that electrons behave like waves and the position of the electron inside the atom can easily be defined with the help of the wave theory of quantum mechanics by solving the Schrodinger wave equation at the specific energy level of an atom.
These wave functions that define the position of an electron inside an atom are called atomic orbitals. These orbitals are the places that have the highest probability of finding the electron. There are four types of orbitals inside an atom
- s - orbital
- p - orbital
- d - orbital
- f - orbital
Atomic orbitals are also defined as the physical space inside the atom where the probability of finding the electron is highest.
Read More:
Three other rules and principles in chemistry help us understand the position, path, orbits and energy levels of electrons in an atom, these are discussed in subsequent subsections:
Aufbau Principle
The Aufbau principle, also called the Aufbau rule, says that electrons go into lower-energy atomic orbitals first before higher-energy ones. "Aufbau" means "building-up" in German.
NCERT Definition of Aufbau Principle
In the ground state of the atoms, the orbitals are filled in order of their increasing energies.
The Aufbau principle helps us figure out how electrons arrange themselves in atoms or ions. For instance, the 1s subshell gets filled up before the 2s subshell.
Here's the order in which electrons fill up the orbitals: 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p, 7s, 5f, 6d, 7p, and so forth. This filling pattern applies to every atom.
For example, using the Aufbau Principle, the electronic configuration of sulfur is written as [S] = 1s2 2s2 2p6 3s2 3p4.
Hund's Rule of Maximum Multiplicity
Hund's rule says that each orbital in a sublevel gets one electron before any of them get a second one. And all the electrons in these single-occupied orbitals have the same spin.
NCERT Definition of Hund's Rule
Pairing of electrons in the orbitals belonging to the same subshell (p, d or f) does not take place until each orbital belonging to that subshell has got one electron each i.e., it is singly occupied.
Hund's rule, also called the maximum multiplicity rule, can result in atoms having multiple unpaired electrons. These unpaired electrons can spin in different directions, creating magnetic moments in various directions.
Hund's rule applies to certain molecules that have unpaired electrons.
Pauli Exclusion Principle
The Pauli exclusion principle says that two identical particles with half-integer spins can't be in the same quantum state within a system.
NCERT Definition of Pauli Exclusion Principle
No two electrons in an atom can have the same set of four quantum numbers.
OR
Only two electrons may exist in the same orbital and these electrons must have opposite spin.
In chemistry, the Pauli exclusion principle tells us that within the same atom, no two electrons can have all four of their quantum numbers identical. This means that at most, two electrons can occupy the same orbital, and they must have opposite spins.
The Pauli exclusion principle sets limits on how many electrons can be in a shell or a subshell.
Solved Questions on Quantum Numbers
Questions 1: Find all four quantum numbers of the last electron of the Rubidium.
Solution:
Rubidium has the atomic number, Z = 37.
Electronic Configuration of Rubidium,
1s2 2s2 2p6 3s2 3p6 3d10 4s2 4p6 5s1
Valence last shell electron is 5s1
Therefore,
Principal Quantum Number, n = 5,
Azimuthal Quantum Number, l = 0,
Magnetic Quantum Number, ml = 0,
Spin Quantum Number, s = +1/2
Questions 2: State the possible values of the magnetic quantum number for l = 2.
Solution:
Given that, the Azimuthal Quantum Number, l = 2
We know that,
ml = - l to + l
Therefore,
ml = -2 to +2
i.e.
m2 = -2, -1, 0, +1, +2
Questions 3: Find all four quantum numbers of the last electron of the Sodium.
Solution:
Sodium has the atomic number, Z = 11.
Electronic Configuration of Rubidium,
1s2 2s2 2p6 3s1
Valence shell last electron is 3s1
Therefore,
Principal Quantum Number, n = 3,
Azimuthal Quantum Number, l = 0,
Magnetic Quantum Number, ml = 0,
Spin Quantum Number, s = +1/2
Questions 4: State the possible values of the magnetic quantum number for l = 3.
Solution:
Given that, the Azimuthal Quantum Number, l = 3
We know that,
for l = 3,
ml = - 3 to + 3
i.e.
m = -3, -2, -1, 0, +1, +2 +3
Quantum Numbers MCQs Practice Problems
To learn more about Quantum Numbers Practice MCQs on Quatum Numbers
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Importance of pH in Everyday LifeAcids, bases, and salts have an impact on chemistry as well as our daily lives. Acids have a sour flavour (the word acid comes from the Latin word ‘acere’ which means ‘sour’), bases have a bitter taste, while salts themselves have a salty taste. Citric acid is found in fruits such as oranges and lem
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Strength of AcidsAcids are a molecule or other species which can donate a proton or accept an electron pair in reactions. When acids react with H2O, they create hydrogen ions; the strength of an acid is determined by the concentration of hydrogen ions in a solution. A higher number of hydrogen ions indicates that th
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Buffer SolutionBuffer Solution is a special aqueous solution that resists the change in its pH when some quantity of acid and Base is added. Many fluids, such as blood, have specific pH values of 7.14, and variations in these values indicate that the body is malfunctioning. The change in pH of Buffer Solutions on
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Solubility EquilibriaThe word "solubility product" refers to inexpensively soluble salts. It is the greatest product of the molar concentration of the ions (raised to their appropriate powers) produced by compound dissociation. The solubility product is constant at any given temperature. The lower the solubility product
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Chapter 8 Redox Reactions
Chapter 9 Hydrogen
Dihydrogen - Structure, Properties and ApplicationsThe lightest element is hydrogen. Under normal conditions, hydrogen is a gas composed of diatomic molecules with the formula H2. It is colourless, odourless, non-toxic, and extremely flammable. Hydrogen is the most abundant chemical element in the universe, accounting for roughly 75% of all normal m
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Isotopes of HydrogenIsotopes of an atom are variants of the same atom but with different mass numbers. That is if two atoms have the same atomic number but different mass numbers then they are called the isotopes of one another. Various examples of the isotopes are the isotopes of hydrogen, we have three different isot
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HydridesHydride in Chemistry is the name of a compound containing Hydrogen Anion. Hydrides are chemical compounds with one atom of hydrogen and an extra atom. Hence, they are an anion of Hydrogen. An anion is a species that has extra electrons and thus exhibits a negative charge. Thus, hydride (hydrogen ani
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Structure and Properties of WaterWater is a valuable natural resource. Water is essential for the survival of all living things. We can't imagine a world without water. Water is required by animals and plants to complete their daily metabolic activities. Water is required by plants to synthesize their food through the photosynthesi
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Chemical Formula of Water - Structure, Properties, Uses, Sample QuestionsHydrogen (H) has unique kind properties that are not like some other component on our planet, close to 66% of our Universe's mass is made out of this unique component. It is both electropositive as well as electronegative, as it structures hydrogen particles (H+)as well as hydride particles (H-). Hy
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Dihydrogen as Fuel - Definition, Uses, ExamplesHydrogen is the first element on the modern periodic table. It has the simplest atomic structure as compared to all other elements. In atomic form, it has one proton and one electron. On the other hand, in elemental form, it exists as a diatomic (H2) molecule called dihydrogen. If Hydrogen loses its
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Chapter 10 S-block Elements
Alkali MetalsAlkali metals are the first group of s-block elements that are found on the leftmost side of the periodic table. Alkali metals are the most electropositive elements on the periodic table as they easily lose electrons. These metals formed various useful compounds with halides, oxygen, and sulfur. Alk
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Characteristics of the Compounds of Alkali MetalsThere are a large number of elements around us having different properties and different uses based on those properties. For using these elements, properties are important so there should be some table to group these elements. This table is known as a periodic table which is created by using the wor
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Anomalous Behavior of Lithium and BerylliumElements are arranged in a periodic table row-wise and column-wise according to similarities in their chemical and physical properties. The elements in the first column are known as Group 1 elements which have the following elements lithium, sodium, potassium, rubidium, Caesium and Francium. All the
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Some Important Compounds of SodiumSodium is a soft metal, it is the eleventh element in the periodic table. It is represented by the Na symbol and the atomic number of sodium is 11 it belongs to the family of s-block elements in the periodic table. Sodium is the sixth most abundant element. Its amount in the earth's crust is nearly
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What is Sodium Chloride? - Definition, Preparation, Properties, UsesSalt's chemical name is sodium chloride. Sodium is an electrolyte that regulates your body's water content. Sodium is also involved in nerve impulses and muscle contractions. Sodium chloride is a medication used to treat or prevent sodium loss caused by dehydration, excessive sweating, or other fact
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Alkaline Earth MetalsAlkaline Earth Metals are Group 2 elements which includes a collection of elements Beryllium, Magnesium, Calcium, Barium, Strontium, and Radium, which are soft silver metals with a less metallic quality than Group 1 alkali metals. All the heavier metals in Group II such as Ca, Sr, Ba, and Ra, share
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Characteristics of the Compounds of Alkaline Earth MetalsAll the elements that exist in nature are arranged in a periodic table after several years of research work, these are placed in groups and rows based on some predefined criteria. Some elements may not follow the criteria but still, they are placed in the same column or group due to their similariti
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Anomalous Behavior of Lithium and BerylliumElements are arranged in a periodic table row-wise and column-wise according to similarities in their chemical and physical properties. The elements in the first column are known as Group 1 elements which have the following elements lithium, sodium, potassium, rubidium, Caesium and Francium. All the
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Some Important Compounds of CalciumCalcium is a reactive alkaline earth metal that when exposed to the air generates a black oxide-nitride coating. Its physical and chemical properties are most similar to those of strontium and barium, its heavier homologues. After iron and aluminium, it is the fifth most abundant element in the Eart
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Plaster of ParisPlaster of Paris is a well-known chemical compound that is widely used in sculpting materials and gauze bandages. While we have seen numerous applications of this substance in our daily lives, Plaster of Paris is a white powdered chemical compound that is hydrated calcium sulphate that is typically
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Biological Importance of Alkali and Alkaline Earth MetalsElements are arranged in a periodic table row-wise and column-wise according to similarities in their chemical and physical properties. The elements in the first column are known as Group 1 elements which have the following elements lithium, sodium, potassium, rubidium, Caesium and Francium. All the
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