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Quantum numbers can be used to describe an electron's trajectory and movement within an atom. On adding the quantum numbers of all the electrons present in a particular atom, they must satisfy the Schrodinger equation. There are four types of quantum numbers which are known as principle, azimuthal, magnetic and spin quantum numbers.
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Quantum Numbers
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A quantum number is a value used to describe the amount of energy available in atoms and molecules. Furthermore, an electron within an ion or an atom has four of these numbers to represent its energy state. It also provides clarifications to Schrodinger's wave equation for hydrogen atoms. The four quantum numbers are as follows -
The principal quantum number is denoted by the letter n.
The Orbital angular momentum quantum number or azimuthal quantum number is denoted by l.
The magnetic quantum number is denoted by the symbol ml.
The electron spin quantum number is denoted by ms.
Furthermore, each electron in an atom has a unique set of quantum numbers. These four quantum numbers and their combinations cannot be the same in two electrons, according to the 'Pauli exclusion principle.'
In addition, these quantum numbers are critical because they are used to understand an atom's electron configuration. They indicate the possible location of an atom's electrons. Additionally, the significance of the quantum number is that it can be used to gather information on atomic properties such as radius and ionisation energy.
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Quantum Numbers Detailed Video Explanation:
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Background of Quantum Numbers
Broglie and Bohr work established that electrons have discrete energy levels associated with their atomic radius. This model provided a more straightforward spherical view. Furthermore, Bohr and Broglie's model demonstrated how electron energy levels are related to their principal quantum number. However, no numerical methods are provided in this model to classify additional behaviour of an electron in space.
Furthermore, Schrodinger's equation provided three additional quantum numbers to describe the behaviour of an electron in a more complex multi-electron atom. This model was diametrically opposed to what Bohr and Broglie had previously proposed. Furthermore, it opened up new avenues for research into quantum numbers.
The Hund-Mulliken theory has also been developed based on these two models and additional contributions from John Lennard-Jones and Slater. Furthermore, this theory is regarded as the most prominent nomenclature system in the history of quantum mechanics. Moreover, this nomenclature follows the Hund-Mulliken theory along with Bohr's energy levels, and the observations on electron spin on spectroscopy and Hund's rule.
Priciple Quantum Numbers
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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 (states a greater atomic size).
The value of the principal quantum number can be any integer having a positive value which is 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 filled with energy and is in an excited state, the electron moves from one principal shell to a higher shell, increasing the value of n. Similarly, when an electron loses its energy, they move to the lower shells, decreasing the value of n.
Absorption refers to the increase in the value of n for an electron, emphasising the photons of energy absorbed by the electron. In the similar manner, when the value of n decreases, an electron is referred to as emission, and this is where the electrons emit their energy.
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Azimuthal Quantum Numbers
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The azimuthal quantum number (or orbital angular momentum quantum number) 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).
Magnetic Quantum Numbers
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Magnetic quantum numbers express the amount of energy available in a subshell and estimate orbital angular momentum along a specific axis. Furthermore, the values associated with ml range from – to l, but only integer steps are associated. In addition, the 's' is a subshell with one orbital where l=0. As a result, ml of an electron within a 's' subshell is always zero.
Furthermore, the 'p' subshell, i.e. l=1, has three orbitals. It's also referred to as three 'dumbbell-shaped' clouds. As a result, an electron's ml in this 'p' subshell should be either -1, 0 or 1.
Finally, the 'd' subshell has five orbitals when l=2. In addition, ml has values ranging from -2 to +2. Moreover, the value of the ml quantum number here is related to orbital orientation.
electron Spin Quantum Numbers
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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,' and is denoted by the symbol ↑. If ms is negative, the electron in question is said to have a downward spin, or 'spin down,' as denoted by the symbol ↓.
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 is generalizable to ±1/2.
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Things to Remember
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- Quantum numbers can be used to describe an electron's trajectory 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 classified into four types: principal, azimuthal or angular momentum, magnetic, and spin quantum numbers. Every number has unique characteristics and a unique value system.
- To completely describe an electron in an atom, four quantum numbers are needed: energy (n), angular momentum (l), magnetic moment (ml), and spin (m$).
- According to Hund's rules, it is important to note that it is impossible for two electrons of the same atom to have exactly the same quantum state or exactly the same values of the set of quantum numbers.
Sample Questions
Ques. What Is A Quantum Number? What are the four quantum numbers? (4 marks)
Ans. Quantum numbers can be used to describe an electron's trajectory 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.
The quantum numbers are:
The principal quantum number is denoted by the letter n.
The Orbital angular momentum quantum number or azimuthal quantum number is denoted by l.
The magnetic quantum number is denoted by the symbol ml.
The electron spin quantum number is denoted by ms.
Ques. Who proposed the principal quantum number? (2 marks)
Ans. The concept of energy levels and notation is based on the earlier Bohr model of the atom. Schrodinger's equation transformed the concept of a two-dimensional flat Bohr atom into a three-dimensional wave motion model. Where n = 1, 2, 3 is referred to as the main quantity, and h is the constant of Planck.
Ques. How many Types of Quantum Number are there? What is the significance of quantum numbers? (5 marks)
Ans. Quantum numbers are classified into four types: principal, azimuthal or angular momentum, magnetic, and spin quantum numbers. Every number has unique characteristics and a unique value system.
The importance of quantum numbers are:
- The quantum numbers are critical because they are used to understand an atom's electron configuration.
- They indicate the possible location of an atom's electrons.
- Additionally, the significance of the quantum number is that it can be used to gather information on atomic properties such as radius and ionisation energy.
Ques. Why are there only eight electrons in the outer shell? (2 marks)
Ans. The stability of an atom's eight electrons is derived from the stability of noble gases, also known as inert gases or unreactive gases. This law, on the other hand, is justified in the periodic table for second row elements with an outermost-shell capacity of 8 electrons.
Ques. How do you find the principal quantum number? (2 marks)
Ans. The principal quantum number n value is the level of the central electronic shell (central level). All orbitals with the same n value are at the same key stage. For example, all orbitals on the second main stage have a principal quantity of n=2.
Ques. What is The Principal Quantum Number? (2 marks)
Ans. The primary quantum number represents the number of electron shells or energy levels within an atom. Furthermore, the value of 'n' here starts at one and gradually increases until it reaches the outermost electron of a specific atom.
Ques. State the Azimuthal Quantum Number. (3 marks)
Ans. The azimuthal quantum number (or orbital angular momentum quantum number) 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).
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