Question

Which quantum number is not associated with the Schrodinger equation?
\[
  a.{\text{ Azimuthal}} \\
  {\text{b}}{\text{. principal}} \\
  {\text{c}}{\text{. magnetic}} \\
  {\text{d}}{\text{. spin}} \\
 \]

Answer 1

Hint: The quantum model of atoms was established with the help of dual nature of matter and Heisenberg’s uncertainty principle. It came into picture as it is a branch of science that takes into account the dual behaviour of matter like electrons.

Complete answer:
Quantum mechanical models give a successful picture of the structure of the atom. The following are the features of quantum mechanical models;
 \[{\text{1}}{\text{.}}\] The energy of electrons is quantized that means that a certain amount of energy is associated with the electron present around the nucleus.
 \[{\text{2}}{\text{.}}\] The electrons are only present in quantized energy levels which are a direct result of the wave-like properties of electrons and are permissible solutions of Schrodinger wave equation.
\[{\text{3}}{\text{.}}\] It replaces the concept of fixed circular orbits or trajectories by the probability of finding the electron at different points in an atom.
\[{\text{4}}{\text{.}}\] The wave function \[\psi \] is also found by solving the Schrodinger wave equation.
Schrodinger equation when applied to multi electron atoms, the result obtained was not correct. The difference lies in the consequence of increased nuclear charge. The results in contraction of the orbitals. The energy of hydrogen-like species depends only on the principal quantum number, whereas the energies of the orbitals in multi-electron atoms depend on both principal quantum number and azimuthal quantum number.
Hence, spin quantum number does not relate to this model.

Note:
Wave function\[\psi \] has as such no physical significance but the square of wave function that is \[{[\psi ]^2}\] known as probability density which gives the probability of finding an electron at a point within an atom.