As we move along the periodic table from left to right the atomic size decreases. However, noble gases have the largest size because of

van der Wall’s radii

The correct answer is option 3. van der Wall’s radii.

When considering the size of atoms across the periodic table, it’s essential to understand the different ways atomic size can be measured. The key reason noble gases appear to have a larger size compared to other elements in the same period is due to the specific measurement of atomic size known as the Van der Waals radius. Let’s break this down:

Atomic Size and Its Measurements

1. Covalent Radius: This is half the distance between the nuclei of two atoms bonded together in a molecule. This measurement is relevant for elements that form covalent bonds, which noble gases generally do not.

2. Ionic Radius: This refers to the size of an atom's ion. It varies depending on whether the atom loses or gains electrons to form a cation or an anion. Noble gases are typically not measured this way because they rarely form ions.

3. van der Waals Radius: This is the distance between the nuclei of two adjacent, non-bonded atoms. For noble gases, which do not readily form bonds, the Van der Waals radius is the most relevant measure. This radius reflects the space an atom occupies when it is not bonded to another atom, which is particularly applicable to noble gases in their gaseous state.

Noble Gases and Atomic Size

Noble Gases: Elements in Group 18 of the periodic table (e.g., helium, neon, argon) are characterized by having a complete valence shell of electrons. This stable configuration means they have little tendency to gain or lose electrons and thus do not form covalent or ionic bonds readily.

van der Waals Radii: Because noble gases are typically encountered in a non-bonded state (like in their gaseous forms), their atomic size is best represented by the Van der Waals radius. This radius is larger than the covalent or ionic radius because it includes the entire extent of the electron cloud when no bonding interactions are compressing it.

Why Noble Gases Appear Larger

As we move from left to right across a period, atoms generally become smaller due to increasing nuclear charge, which pulls electrons closer to the nucleus. However, the noble gases at the end of each period seem to buck this trend when looking at atomic sizes measured by Van der Waals radii.

Stable Octet: The noble gases have a full valence shell, contributing to their lack of reactivity. While this "stable octet" is a reason for their chemical inertness, it’s not the direct reason for their larger atomic size.

Measurement Perspective: The larger size of noble gases is more an artifact of the method of measurement. Van der Waals radii measure the space that an atom’s electron cloud occupies when it is in close, non-bonded contact with another atom. Since noble gases do not form bonds and their electron clouds are relatively unperturbed by bonding forces, their Van der Waals radii are larger.

In summary, the apparent larger size of noble gases when compared to their neighbors is due to the use of Van der Waals radii as the measure of their atomic size. This method reflects the space an atom occupies in its non-bonded state, which is relevant for noble gases and leads to their larger measured atomic size compared to other elements where covalent or ionic radii are used. Therefore, the correct answer is van der Waals radii