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Quantum Numbers – Concept, Types, Examples

  • Difficulty Level : Hard
  • Last Updated : 29 Nov, 2021

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 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. Electronic quantum numbers (quantum numbers describing electrons) are a set of numerical values that provide solutions to the Schrodinger wave equation for hydrogen atoms.

Four quantum numbers can be used to fully describe all of the properties of a given electron in an atom; these are:

  1. Principal quantum number
  2. Orbital angular momentum quantum number (or azimuthal quantum number).
  3. Magnetic quantum number
  4. The electron spin quantum number

Principal Quantum Number

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 principle 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

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

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 and +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

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.

Sample Questions 

Question 1: Who proposed the principal quantum number?


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 Planck constant.

Question 2: What is Quantum Energy?


In mechanics, a quantum is a discrete natural unit or bundle of energy, charge, angular momentum, or other physical property. Photons, which are particle-like packets of light, are a concept that is frequently applied to quanta with other sources of electromagnetic radiation such as X rays and gamma rays.

Question 3: What is magnetic polarization?


Magnetization or magnetic polarisation is the vector field that represents the density of permanent or induced magnetic dipole moments in a magnetic medium in classical electromagnetism. M is represented by a pseudovector.

Question 4: What is the spin of an electron?


Electron spin is a quantum property of electrons. It is a shape with angular momentum. As a teaching technique, instructors compare electron spin to the planet rotating on its own axis every 24 hours. Spin-up occurs when the electron spins clockwise on its axis; spin-down occurs when the electron spins counterclockwise.

Question 5: What are the principal energy levels?


The shell or orbital in which an electron resides relative to the nucleus of the atom is referred to as the electron’s primary energy level in chemistry. This level is denoted by the principal quantum number n. The first element of the periodic table introduces a new key energy level.

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