Quantum Numbers

The allowed subshells under different combinations of ‘n’ and ‘l’ are listed above. It can be understood that the ‘2d’ orbital cannot exist since the value of ‘l’ is always less than that of ‘n’.

• 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, as per Hund’s rules.

• Who proposed the principal quantum number?

• The notion of energy levels and notation has been taken from the atom ‘s earlier Bohr model. Schrodinger ‘s equation evolved the concept from a two-dimensional flat Bohr atom to a three-dimensional model for wave motion. Where n = 1 , 2 , 3 is called the main quantity, and h is the constant of Planck.

• Why are there only 8 electrons in the outer shell?

• The stability of an atom ‘s eight-electrons derives from the stability of the noble gases or the elder term of inert gases, also known as unreactive or noble gases. This law, however, is justified in the periodic table for second row elements whose outermost-shell capacity is 8 electrons.

• How do you find the principal quantum number?

• 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. All orbitals on the second main stage , for example, have a principal quantity of n=2.

• What are the principal energy levels?

• In chemistry, an electron’s primary energy level refers to the shell or orbital in which the electron resides relative to the nucleus of the atom. The principal quantum number n denotes this level. Within a time of the periodic table the first element introduces a new key energy level.

• Which energy level has the least energy?

• There is a single 1s orbital that can accommodate 2 electrons at the lowest energy level, the one nearest to the atomic core. There are four orbitals at the next energy level; a 2s, 2p1, 2p2 and a 2p3. Each of these orbitals can carry 2 electrons, so we can find a total of 8 electrons at this energy level.

• What is Quantum Energy?

• Quantum, in mechanics, of energy, charge, angular momentum, or other physical property, discrete natural unit, or bundle. Photons, a concept often applied to quanta with other sources of electromagnetic radiation such as X rays and gamma rays, are certain particle-like packets of light.

• What is magnetic Polarisation?

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

• What is the spin of an electron?

• A quantum property of electrons is electron spin. It is an angular momentum shape. Instructors also equate electron spin to the planet rotating on its own axis every 24 hours as a teaching technique. If the electron spins on its axis clockwise, it is known as spin-up; spin-down is counterclockwise.

• What is the Aufbau Principle?
  The Aufbau principle dictates the manner in which electrons are filled in the atomic orbitals of an atom in its ground state. It states that electrons are filled into atomic orbitals in the increasing order of orbital energy level. According to the Aufbau principle, the available atomic orbitals with the lowest energy levels are occupied before those with higher energy levels.
  The word ‘Aufbau’ has German roots and can be roughly translated as ‘construct’ or ‘build up’. A diagram illustrating the order in which atomic orbitals are filled is provided below. Here, ‘n’ refers to the principal quantum number and ‘l’ is the azimuthal quantum number.

• The Aufbau principle can be used to understand the location of electrons in an atom and their corresponding energy levels. For example, carbon has 6 electrons and its electronic configuration is 1s22s22p2.
  It is important to note that each orbital can hold a maximum of two electrons (as per the Pauli exclusion principle). Also, the manner in which electrons are filled into orbitals in a single subshell must follow Hund’s rule, i.e. every orbital in a given subshell must be singly occupied by electrons before any two electrons pair up in an orbital.
  Salient Features of the Aufbau Principle

  • According to the Aufbau principle, electrons first occupy those orbitals whose energy is the lowest. This implies that the electrons enter the orbitals having higher energies only when orbitals with lower energies have been completely filled.

  • The order in which the energy of orbitals increases can be determined with the help of the (n+l) rule, where the sum of the principal and azimuthal quantum numbers determines the energy level of the orbital.

  • Lower (n+l) values correspond to lower orbital energies. If two orbitals share equal (n+l) values, the orbital with the lower n value is said to have lower energy associated with it.

  • The order in which the orbitals are filled with electrons is: 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p, 7s, 5f, 6d, 7p, and so on.

• Exceptions
  The electron configuration of chromium is [Ar]3d54s1 and not [Ar]3d44s2 (as suggested by the Aufbau principle). This exception is attributed to several factors such as the increased stability provided by half-filled subshells and the relatively low energy gap between the 3d and the 4s subshells.
  Half filled subshells feature lower electron-electron repulsions in the orbitals, thereby increasing the stability. Similarly, completely filled subshells also increase the stability of the atom. Therefore, the electron configurations of some atoms disobey the Aufbau principle (depending on the energy gap between the orbitals).
  For example, copper is another exception to this principle with an electronic configuration corresponding to [Ar]3d104s1. This can be explained by the stability provided by a completely filled 3d subshell.
  Electronic Configuration using the Aufbau Principle
  Writing the Electron Configuration of Sulphur

  • The atomic number of sulphur is 16, implying that it holds a total of 16 electrons.

  • As per the Aufbau principle, two of these electrons are present in the 1s subshell, eight of them are present in the 2s and 2p subshell, and the remaining are distributed into the 3s and 3p subshells.

  • Therefore, the electron configuration of sulphur can be written as 1s22s22p63s23p4.

• Writing the Electron Configuration of Nitrogen

  • The element nitrogen has 7 electrons (since its atomic number is 7).

  • The electrons are filled into the 1s, 2s, and 2p orbitals.

  • The electron configuration of nitrogen can be written as 1s22s22p3

• To learn more about the Aufbau principle and other related concepts (such as the octet rule),

• Hund’s rule of maximum multiplicity
  The rule states that, for a stated electron configuration, the greatest value of spin multiplicity has the lowest energy term. It says if two or more than two orbitals having the same amount of energy are unoccupied then the electrons will start occupying them individually before they fill them in pairs. It is a rule which depends on the observation of atomic spectra, which is helpful in predicting the ground state of a molecule or an atom with one or more than one open electronic shells. This rule was discovered in the year 1925 by Friedrich Hund.
  Uses of Hund’s Rule:
  It has wide applications in the following –
  It is majorly used in atomic chemistry, quantum chemistry, and spectroscopy, etc.

• Explanation of Hund’s Rule
  The electrons enter an empty orbital before pairing up. The electrons repel each other as they are negatively charged. The electrons do not share orbitals to reduce repulsion.
  When we consider the second rule, the spins of unpaired electrons in singly occupied orbitals are the same. The initial electrons spin in the sub-level decides what the spin of the other electrons would be. For instance, a carbon atom’s electron configuration would be 1s22s22p2. The same orbital will be occupied by the two 2s electrons although different orbitals will be occupied by the two 2p electrons in reference to Hund’s rule.

• An electron will not pair with another electron in a half-filled orbital as it has the ability to fill all its orbitals with similar energy. Many unpaired electrons are present in atoms which are at the ground state. If two electrons come in contact they would show the same behaviour as two magnets do. The electrons first try to get as far away from each other as possible before they have to pair up.

• What is Pauli Exclusion Principle?
  Pauli exclusion principle states that in a single atom no two electrons will have an identical set or the same quantum numbers (n, l, ml, and ms). To put it in simple terms, every electron should have or be in its own unique state (singlet state). There are two salient rules that the Pauli Exclusion Principle follows:

  • Only two electrons can occupy the same orbital.

  • The two electrons that are present in the same orbital must have opposite spins or it should be antiparallel.

• However, Pauli Exclusion Principle does not only apply to electrons. It applies to other particles of half-integer spin such as fermions. It is not relevant for particles with an integer spin such as bosons which have symmetric wave functions. Moreover, bosons can share or have the same quantum states, unlike fermions. As far as the nomenclature goes, fermions are named after the Fermi–Dirac statistical distribution that they follow. Bosons, on the other hand, get their name from the Bose-Einstein distribution function.

• Pauli Exclusion Principle Example
  We can take a neutral helium atom as a common Pauli Exclusion Principle example. The atom has 2 bound electrons and they occupy the outermost shell with opposite spins. Here, we will find that the two electrons are in the 1s subshell where n = 1, l = 0, and ml = 0.
  Their spin moments will also be different. One will be ms = -1/2 and the other will be +1/2. If we draw a diagram then the subshell of the helium atom will be represented with 1 “up” electron and 1 “down” electron. In essence, 1s subshell will consist of two electrons, which have opposite spins.

• Introduction to Quantum Numbers
  Every electron in an atom can be defined completely by quantum numbers. Quantum numbers are values that describe the state of an electron, such as the electron shell, the shape of the orbital, orientation and number of orbitals and the electronic spin. There are four quantum numbers that are used.

  • n is the principal quantum number. It talks about the position of the electron in the innermost shell.

  • l is said to be the orbital angular momentum quantum number and helps us determine the shape of an orbital.

  • ml is expressed as magnetic quantum number and it reveals the number of orbitals and their orientation.

  • ms denotes the spin quantum number and it identifies the direction of the electron spin.