Question

Which orbital is represented by the complete wave function $ {{\psi }_{420}} $ ?
A) 4d
B) 3d
C) 4p
D) 4s

Answer 1

Hint: An atomic orbital is a mathematical function in atomic theory and quantum physics that describes the position and wave-like behaviour of an electron in an atom. This function may be used to determine the likelihood of locating any atom's electron in any given area surrounding the nucleus. The phrase atomic orbital can also refer to the actual region or space in which the electron can be calculated to be present, based on the orbital's mathematical structure.

Complete answer:
Each orbital in an atom has its own set of values for the three quantum numbers n, l, and $ {{m}_{l}} $ , which correspond to the electron's energy, angular momentum, and an angular momentum vector component, respectively (the magnetic quantum number). Each of these orbitals may hold a maximum of two electrons, each having its own spin $ {{m}_{s}} $ projection. The terms s orbital, p orbital, d orbital, and f orbital all refer to orbitals having angular momentum quantum numbers of 0, 1, 2, and 3, respectively.
Although for higher values of the quantum number n, particularly when the atom in question bears a positive charge, the energies of certain sub-shells become very sizable, the repeating periodicity of the blocks of 2, 6, 10, and 14 elements within sections of the periodic table arises naturally from the total number of electrons that occupy a complete set of s, p, d, and f atomic orbitals, respectively.
The wave function $ \psi $ n,l,m is used to represent orbitals.
The wavefunction in question is $ {{\psi }_{420}} $ .
As a result, n=4 and l=2d-orbital
As a result, the orbital is 4d.
Option (A) is correct.

Note:
The circling electrons around a nucleus could not be properly characterised as particles due to the development of quantum mechanics and experimental results (such as the two slit diffraction of electrons), and had to be explained by the wave-particle duality. In this way, electrons possess both characteristics.