A neutral atom of an element has \(2 K, 8 L, 9 M\) and \(2 N\) electrons. Find out the following: (a) Atomic no., (b) Total no. of \(s\) -electrons, (c) Total no. of \(p\) -electrons, (d) Total no. of \(d\) -electrons, (e) Valency of element, (f) No. of unpaired electrons.

Understanding the atomic number of an element is fundamental in studying chemistry, especially in preparing for competitive exams like IIT-JEE. The atomic number, symbolized as 'Z', refers to the number of protons present in an element's nucleus. This number is incredibly significant because it defines the chemical identity of an element and determines its position in the periodic table.

For a neutral atom, which means the atom has no charge, the number of protons is equal to the number of electrons. Therefore, to determine the atomic number of a neutral atom, you simply count the number of electrons distributed among the various shells or energy levels. For example, if the electronic configuration of an atom is given as '2 K, 8 L, 9 M, and 2 N', adding up these numbers: 2 + 8 + 9 + 2, will give you the atomic number, which is 21 in this case. This number tells you that the corresponding element is Scandium on the periodic table, key information for subsequent chemistry-related analyses.

Electron configuration is a description of the distribution of electrons in the atomic orbitals of an atom. It's crucial for predicting the chemical, electrical, and magnetic behavior of an atom. The electrons are arranged in shells around the nucleus, with each shell being designated by letters K, L, M, N, and so on.

Electrons fill the shells starting from the innermost (K) to the outermost (N), and each shell has subshells (s, p, d, f) which have a specific number of orbitals that can be filled. In detail, the 's' subshell can hold 2 electrons, the 'p' subshell can hold 6, the 'd' for 10, and the 'f' for 14 electrons.

For instance, an atom with an electronic configuration of '2 K, 8 L, 9 M, and 2 N' will have filled 's' orbitals in every shell, while reaching the 'p' orbitals in the L and M shells. To count total s- or p-electrons, you count how many electrons are in each corresponding subshell across all energy levels.

Valency is a concept that describes the ability of an element to combine with other elements, synonymous with the number of bonds an atom of an element can form. It depends on the number of electrons in the outermost shell (valence shell) and how close this number is to the magic number 8 (in the case of the main group elements related to the octet rule).

Calculating valency can typically be done by determining how many electrons are needed to either fill or half-fill the valence shell. When the outer shell contains fewer than 4 electrons, the valency is equal to that number, indicating that it tends to lose electrons. Conversely, if there are more than 4 electrons, the valency is calculated by subtracting from 8, signifying a tendency to gain electrons to achieve stability.

For example, with 2 electrons in the outermost (N) shell, the valency of the element can be asserted as 2, showing it needs two more electrons to complete the pair or lose two to achieve a filled or half-filled configuration.

Unpaired electrons are critical markers in atomic structure, as they play a significant role in defining the magnetic properties of an atom. These are the electrons in an atom that are not part of a pair inside an orbital. Atoms with unpaired electrons exhibit paramagnetism (attraction to magnetic fields) due to these unpaired spins.

Calculating unpaired electrons requires knowledge of the electron configuration and pairing principles. Electrons pair up only after each available orbital in a subshell is singly occupied. Therefore, to ascertain the number of unpaired electrons, you must check the electron configuration and pairing situation in each subshell.

For the electronic configuration '2 K, 8 L, 9 M, and 2 N', and assuming the orbitals are filled according to Hund's Rule (where one electron will occupy an orbital before electrons pair up), it appears that there are no unpaired electrons. This is because the s-orbitals are completely filled in pairs, and there is no mention of unpaired electron scenarios in p, d, or f orbitals based on the given configuration and common electron pairing behavior.