Question

The sum of all the quantum numbers of all the valence electrons of an atom of an inert gas is 22. Identify the inert gas:
A.Helium
B.Neon
C.Argon
D.Krypton

Answer 1

Hint: Write the electronic configuration of all the gases and pick out the similar pattern for valence shells. Then count the no. of electrons present in them and correspondingly we will calculate all the quantum numbers.

Complete step By Step Solution:
Electronic configuration of Helium is \[1{{s}^{2}}\]
Electronic configuration of Neon is \[1{{s}^{2}}2{{s}^{2}}2{{p}^{6}}\]
Electronic configuration of Argon is \[1{{s}^{2}}2{{s}^{2}}2{{p}^{6}}\] \[3{{s}^{2}}3{{p}^{6}}\]
Electronic configuration of Krypton is \[\left[ Ar \right]\] \[3{{d}^{10}}4{{s}^{2}}4{{p}^{6}}\]
So, it can be seen that valence shell configuration for inert gases is (\[n{{s}^{2}}n{{p}^{6}}\])
So, there are total 8 electrons, so Sum of principal quantum no\[\left( n \right)\text{ }=8n\] Sum of azimuthal quantum no(l)= \[2\times \](value of l for s-orbital)+ 6\[\times \](value of l for p-orbital)
=\[2\times \]0 +6\[\times \]1
= 6
Sum of magnetic and spin quantum numbers \[=\text{ }0\]
So, total sum of quantum no’s
 \[=\text{ }8n\text{ }+\text{ }6\text{ }+\text{ }0\text{ }+\text{ }0\]
\[=\text{ }8n\text{ }+\text{ }6\]
 Given sum = 22. So
$8n + 6 = 22 $
So, n = \[\dfrac{16}{8}\] = 2
So, the configuration we get is \[2{{s}^{2}}2{{p}^{6}}\]. It can be seen that the inert gas is Neon.

So, the correct option is (B).

Additional Information:
Inert Gas: An inert gas is a gas that does not undergo chemical reactions under a set of given conditions. The noble gases often do not react with many substances. The group 18 elements include helium, neon, argon, krypton, xenon and radon. They are referred to as noble gases or inert gases. The general configuration of the valence shell is \[n{{s}^{2}}n{{p}^{6}}\] . All of these elements occur in a free state in the atmosphere. They are colorless, tasteless and odorless gases with low melting and boiling points. They have high positive electron gain enthalpy and high ionization enthalpy.
Because of the non-reactive properties of inert gases they are often useful to prevent undesirable chemical reactions from taking place. Food is packed in inert gas to remove oxygen gas. This prevents bacteria from growing. It also prevents chemical oxidation by oxygen in normal air. Inert gases are often used in the chemical industry. In a chemical manufacturing plant, reactions can be conducted under inert gas to minimize fire hazards or unwanted reactions.
Valence Electrons: a valence electron is an outer shell electron that is associated with an atom, and that can participate in the formation of a chemical bond if the outer shell is not closed. These are the electrons that can be gained or lost during a chemical reaction. The valence electrons are part of most of the chemical reactions because they contain more energy compared to the electrons present in inner orbits. Meanwhile, the number of valence electrons present also helps us determine a specific element’s chemical properties, such as its valence or valence, the formation of bonds with other elements. It also gives us an idea of how readily the atoms can form bonds, the number of unpaired electrons and how many atoms can take part.

Note: Learn how to write the electronic configurations for various elements. The no. of electrons present in their valence shells. Study the Inert Gases, their properties, and their uses. Read about the different types of quantum no’s and their importance, their relation with one another. One can also study the Origin of quantum no’s and the Atomic Models which led to their development.