3.7.1.a. Atomic Radius

You can very well imagine that finding the size of an atom is a lot more complicated than measuring the radius of a ball. Firstly, because the size of an atom (~ 1.2 Å i.e., 1.2 × 10–10 m in radius) is very small. Secondly, since the electron cloud surrounding the atom does not have a sharp boundary, the determination of the atomic size cannot be precise. In other words, there is no practical way by which the size of an individual atom can be measured.

The atomic radius is not easily quantified because atoms are extremely small—so small that typical measuring techniques used for larger objects don't apply. We also cannot pinpoint where an atom ends, as the electrons surrounding it exist in a cloud rather than a fixed shell. This means that measuring these dimensions is inherently uncertain.

Imagine trying to measure the size of a cloud with a ruler. Just as clouds change shape and don't have defined edges, atoms have electron clouds that make measuring their 'size' challenging.

However, an estimate of the atomic size can be made by knowing the distance between the atoms in the combined state. One practical approach to estimate the size of an atom of a non-metallic element is to measure the distance between two atoms when they are bound together by a single bond in a covalent molecule and from this value, the 'Covalent radius' of the element can be calculated.

To overcome the difficulty in measuring atomic size directly, scientists look at how atoms interact in bonds. In a molecule, for example, the distance between two bonded atoms represents a practical way to estimate the size of a single atom when you divide that distance by two. This is known as the covalent radius.

Think of how we can estimate the width of a door by measuring the distance between the door frame. Similarly, we estimate atomic size by measuring the bond lengths in molecules.

For example, the bond distance in the chlorine molecule (Cl2) is 198 pm and half this distance (99 pm) is taken as the atomic radius of chlorine. For metals, we define the term 'metallic radius' which is taken as half the internuclear distance separating the metal cores in the metallic crystal.

Different atomic radii types exist: the covalent radius for non-metals and metallic radius for metals. For chlorine, its atomic radius is half of the distance between the two bonded chlorine atoms. Similarly, the distance between adjacent metal atoms in a crystal gives us the metallic radius.

Imagine measuring a rope by folding it: the length of one fold gives us information about the whole rope. In chemistries, we measure distances in bonds to evaluate atomic sizes by halving those distances.

Two trends are obvious. We can explain these trends in terms of nuclear charge and energy level. The atomic size generally decreases across a period as illustrated for the elements of the second period. It is because within the period, the outer electrons are in the same valence shell and the effective nuclear charge increases as the atomic number increases resulting in the increased attraction of electrons to the nucleus.

As you move left to right across the periodic table, each element has more protons (increased nuclear charge) without a corresponding increase in the distance of valence electrons from the nucleus. This leads to a stronger attraction between the nucleus and the electrons, causing the atomic radius to decrease.

Think of it like a magnet: as you approach the fridge with a magnet, the attractive force between them increases, pulling the magnet closer. In atoms, as protons increase, they pull the surrounding electrons in tighter, shrinking atomic size.

Within a family or vertical column of the periodic table, the atomic radius increases regularly with atomic number. For alkali metals and halogens, as we descend the groups, the principal quantum number (n) increases and the valence electrons are farther from the nucleus. This happens because the inner energy levels are filled with electrons, which serve to shield the outer electrons from the pull of the nucleus.

In a vertical group, as you go down the table, the atoms have more energy levels, which means the outermost electrons are farther from the nucleus. This increased distance, coupled with electron shielding from inner electrons, allows the atomic radius to increase.

Consider how a taller person has arms that are further away from their body than a shorter person. In a similar way, as atoms get more energy levels (or layers of electrons), their 'outer arms'—the outermost electrons—get farther away, increasing atomic size.

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