Atomic Radii

The radius of an atom of a chemical element is a measure of the atom's size. The meaning of it is said as the typical distance which is from the center of the nucleus till the boundary of the atom which is surrounding the electrons. There are three widely used definitions which are used for atomic radius:they are the  ionic radius, Van der Waals radius, and covalent radius.

According to the definition these terms may be applied only to isolated atoms in condensed matter as well covalently which have bonding in molecules or even within ionized and excited states as well. And its value can also be obtained by the experimental measurements, or computed from models of theory. The radius value can even depend on the atom's state.

It is said that the electrons do not have definite orbits or sharply defined ranges. The position of the molecules can be described as probability which has distributions that gradually taper off as one that moves away from the nucleus. And that too without a sharp cutoff. In condensed molecules and matter the cloud of electrons of the atoms usually overlap to some extent, and some of the electrons can even roam over a large region encompassing two or even more atoms.

In most of the definitions of the radii of isolated atoms which are neutral atoms range between 30 and 300 pm  that is trillionths. Or even between 0.3 and 3 ångströms. The radius of atoms is more than 10,000 times the radius of its nucleus that is 1–10 pm and less than 1/1000 of the wavelength of visible light that is 400–700 nm.

Covalent Radius

Here letter r covalent is defined as =  ½  that is the internuclear distance between two bonded atoms. The internuclear distance which is between two bonded atoms is called the bond length. 

Van Der Waals Radius

It is one the distance which is half the distance between the nuclei of two similar non-bonded isolated atoms or even two adjacent identical atoms belonging to two neighboring molecules of an element which are in the solid-state. The weakest forces which are also known as the van der wall magnitude of the radius are dependent on the packing of the atoms when the element is in the solid-state.

An example of the internuclear that is the distance which is between two adjacent atoms of chlorine in the solid-state which is 360 pm. So the Van der Waals radius of the chlorine atom is said to be 180 pm.

Metallic Radius

A crystal contains positive kernel ions which are arranged in a pattern which is definite in a sea of mobile electrons which are valence.The force of attraction which is between electrons that are basically mobile and the positive kernels is also called the metallic bond. It is said to be one of the half internuclear distances which is between the two adjacent metal ions in the lattice metallic. In a metallic lattice the valence electrons are mobile or we can say they are free to move  therefore they are only weakly attracted by the metal ions or kernels.

In a bond-like covalent bond, there is a pair of electrons which is strongly attracted by the nuclei of two atoms. That is why a metallic radius is always longer than its covalent radius. 

General Trends in Atomic Radii in the Elements of the Periodic Table

• The way the atomic radius varies with increasing atomic number is referred to here as the general trends. This trend can be explained by the arrangement of electrons in fixed shells around the nucleus of an atom. The general rule is that shells fill in  the order of increasing radius, since the negatively charged electrons are attracted by the positively charged protons in the nucleus. As the atomic numbers increase(and therefore the total number of protons) along each row of the periodic table, the additional electrons go into the same outermost shell; whose radius gradually contracts, due to the increasing nuclear charge. 

• In elements such as that of a noble gas, the outermost shell of the atom is completely filled; therefore, the additional electron of the next alkali metal enters into the next outer shell, which explains the sudden increase in the atomic radius.

• Thus we notice that for an atom in the periodic table,  increasing charge in the nucleus is partially counterbalanced by the increasing number of electrons in its orbit, a phenomenon that is called the "shielding effect". This effect accounts for the size of atoms which gradually increases down each column in the periodic table. 

• However, there are few notable exceptions. They are the d-block contraction and the f-block contraction (also known as lanthanide contraction). Lanthanide contraction refers to the much smaller size of the 5d block of elements than one would expect which happens due to the poor shielding of the 4f electrons.

• As a thumb rule, the atomic radii decrease across the periods as the total protons in the nucleus increases. There is greater attraction experienced by the orbiting electrons, which draws them closer to the protons, decreasing the size of the atom. Therefore, the atomic radius decreases. 

• Down the groups, atomic radius increases because there are more energy levels and hence a greater space between protons and electrons. In addition to this, electron shielding effect is also observed which causes attraction to decrease and the remaining  (valence) electrons can go farther away from the positively charged nucleus. This causes the size, or atomic radius, to increase.

Explanation

The shells which are present are generally  filled in order of radius which is increasing since the negatively charged electrons are attracted by the positively charged protons in the nucleus. The additional electrons go into the same shell which is the outermost shell whose radius contracts graduall. And this happens mostly due to the increasing nuclear charge. In a noble gas if we keenly observe, the outermost shell is completely filled and therefore the additional electron of the next alkali metal will go into the next outer shell for the increase in the atomic radius.

This explains why the size of atoms usually increases down each column. There is one notable exception for this and is known as the lanthanide contraction that is the 5d block of elements which are much smaller than one would expect which is due to the weak shielding of the 4f electrons.

Notes

The Difference between experimental and empirical data: “Empirical data basically means that they are originating  or we can say they are based on observation or experience that are relying on observation or experience alone often without due regard for system and theory data". It basically means that we measure it through physical observation and a lot of experiments which are generating the same results. Note that the values are not calculated by a formula. But, often the empirical results then become an equation of estimation. Experimental data which are on the other hand are only based on theories.