Periodic Trend Atomic Radius

Atomic radius refers to the size of an atom. It is defined as one-half the distance between between two nuclei in a chemical bond.

Atomic_radius_of_H2.svg

Atomic radius is measured in picometers. 1 picometer is a trillionth of a meter. 1 pm = 10-12 meters. Atomic radii range from 32 pm, the atomic radius of helium, to 348 pm for francium.

As you go down a group in the Periodic Table, atomic radius increases. This is because, with each successive period, another energy level of electrons is being added, moving the outermost electrons further from the nucleus. Consider the first column of the Periodic Table, consisting mostly of the alkali metals (with the notable exception of the nonmetal hydrogen). Hydrogen has 1 valence electron in the first energy level n=1. Lithium has two shells of electrons. The first shell, or energy level, contains two electrons, and the second energy level n=2 contains 1 valence electron. Since the lithium’s valence electron is in the second energy level, it is further from the nucleus than hydrogen’s valence electron. Therefore, the atomic radius of lithium is greater than that of hydrogen. Moving further down the group, sodium has a total of 11 electrons. Sodium’s first two electrons are in the first energy level, n=1. Its next 8 electrons are in the second energy level, n=2. And its one valence electron is in the third energy level n=3. With three energy levels of electrons, sodium’s atomic radius is greater than lithium’s.

atomic-radius-trend

 

As you go across a period in the Periodic Table, atomic radius decreases. This seems counter intuitive because, with each successive element in the Periodic Table another proton and electron is being added. Realize, however, that atoms are mostly empty space, so even though the atomic mass generally increases from element to element, atomic size does not. Within the same period, no new energy levels are being added. With the addition of each subsequent proton in the same period, the nuclear charge — the positive charge of the nucleus — increases. This increased nuclear charge exerts a greater attractive force on the outermost electrons, according to Coulomb’s Law, drawing them closer to the nucleus.

coulombs-law

atomic-radius-period

Li 152 pm

Be 105 pm

B 85 pm

Here is a graph of atomic radius as a function of atomic number.

atomic-radius-vs-atomic-number
(Image from https://upload.wikimedia.org/wikipedia/commons/b/bc/Empirical_atomic_radius_trends.png)

Notice that, between atomic numbers 3 and 9 (Lithium to Fluorine), atomic radius decreases. Lithium through fluorine represent most of the second period of the periodic table. Notice further that sodium Na, the first element of the third period, is larger in atomic radius than lithium, because atomic radius increases as you go down a group.

Periodic Trends and Coulomb’s Law

Periodic Trends describe repeating patterns that help predict certain properties, depending on an element’s location in the Periodic Table. In this section, I will discuss the periodic trends of atomic radius, ionic radius, ionization energy, electronegativity and electron affinity.

In order to better understand Periodic Trends, it is best to explore Coulomb’s law, which describes the force of attraction between opposite charges. Coulomb’s Law states that the force of attraction between two opposite charges is proportional to the strength of those charges, and inversely proportional to the square of the distance between those charges.

coulombs-law
F = force of attraction (or repulsion)
k = proportionality constant
q1 = the magnitude of charge on particle 1
q2 = the magnitude of charge on particle 2
r = distance between the two charged particles

Let’s consider this equation qualitatively. If we increase the charge on either q1 or q2, we increase the magnitude of the attractive force. When we increase the distance between the two charges (r), we decrease the magnitude of the attractive force by a factor of distance squared. Since the denominator is squared, distance has a greater effect on the attractive force than charge. In other words, if charges are too far away from each other to exert a force on each other, the magnitude of their charges becomes insignificant.

Let’s use some fictional numbers to illustrate this. Let’s say q1 represents a nucleus with only one proton, charge +1, and q2 represents a valence electron of charge -1. Recall that a valence electron is an electron in the atom’s outermost energy level or shell. And, let’s say the distance r between the proton and electron is 1 (again, this is a fictional number without units). Plugging these numbers into our equation, we see that the attractive force is proportional to -1:

coulombs-law-1

It is “proportional” to -1 because we haven’t defined what the proportionality constant k is, which would be the same in all instances, since it’s a constant.

Now, let’s say we double the charge on the nucleus by adding another proton, so its charge q1 = +2.

coulombs-law-2

All else being equal, the attractive force has doubled when we double the number of protons in the nucleus.

Let’s see what happens now when we double the distance between the nucleus and the valence electron. When we double the distance between the 1 proton in the nucleus and its outermost electron, the attractive force is reduced to -1/4.

coulombs-law-2charge

This is what scientists refer to as the “inverse square law.” The inverse square law describes a quantity that is inversely proportional to the square of the distance from its source. Other examples of physical entities that observe this law are the force of an electric field on a charge particle, the force exerted by a magnetic field, and the intensity of light.

In terms of periodic trends, we will explore the effects of nuclear charge on certain atomic properties, as well as distance between the nucleus and its outermost valence electrons.

Semi-Metals or Metalloids

The semi-metals, also known as metalloids, are Boron (atomic number 5), Silicon (14), Germanium (32), Arsenic (33), Antimony (51), Tellurium (52) and Polonium (84). They are so named because they share properties of both metals and nonmetals.

As such, they tend to be lustrous (like metals), brittle (as opposed to the malleability and ductility of metals) semiconductors with other properties intermediate between metals and nonmetals.

metalloids

 

Is Astatine a halogen or metalloid?

Depending on whom you ask, astatine is either a halogen or a semimetal. The confusion stems from the short half-life of astatine, the longest-lived isotope having a half-life of only 8.1 hours. It is so radioactive that scientists cannot keep a sample around long enough to assess whether it does indeed have the properties of a metalloid. Rather, the heat generated by its decay melts and vaporizes whatever amount of sample remains.

Transition Metals

The Transition Metals are those elements in groups 3 through 12 on the Periodic Table. They share the properties of all metals, those of malleability, ductility and conductivity. Their highest energy electrons can be found in the “d” sublevel, which allows them many different oxidation states (an oxidation state is another term for the charge of its ion). A few of the transition metals have only one oxidation state. These are silver, which only has the oxidation state +1 (Ag+), and cadmium and zinc, which only have the oxidation state +2 (Cd2+ and Zn2+).

transition-metals

 

 

The Alkaline Earth Metals

The alkaline earth metals are found in the second group of the Periodic Table (IIA).

alkaline-earth

 

As their name suggests, they are metals, so they possess properties common to all metals, such as malleability, ductility and conductivity. Overall though, they are less metallic in nature than the alkali metals, as metallic character decreases as you go left to right across the Periodic Table. The alkaline earth metals are also highly reactive, the heavier metals such as Ca, Sr, Ba, and Ra being almost as reactive as their alkali metal neighbors. The alkaline earth metals have two valence electrons and form the +2 ion.

The Alkali Metals

The first group on the left of the Periodic Table, Group 1 (IA) is known as the Alkali Metals.

alkali-metals

The alkali metals are highly reactive metals that do not exist by themselves in nature. They are highly reactive because they have just one valence electron, which they can easily give up to form an ionic compound. Valence electrons refer to the electrons in their outermost shell. As metals, the alkali metals share properties common to all metals, such as malleability (the ability to be hammered), ductility (the ability to be stretched) and conductivity (metals are good conductors of both heat and electricity). Further, the alkali metals are softer than most other metals. Because of their high reactivity, these metals literally explode in water, and are therefore usually stored in oil to prevent water contact. This is how they got their name. “Alkali” means basic, from the Arabic word “al qali” (from the ashes). When alkali metals react with water, they form hydroxide ions, raising the pH above 7.

Hydrogen, though at the top of the alkali metal group, is NOT an alkali metal. In fact, it’s not a metal at all. But, since it contains one valence electron, and easily gives up that valence electron to form compounds, it is placed here in the periodic table.

Structure of the Modern Periodic Table

The Modern Periodic Table is arranged in order of increasing atomic number, which is the number of protons in the nucleus of an atom. The lightest atom is Hydrogen, in the upper left-hand corner, with an atomic number of 1. This means that hydrogen contains only 1 proton in its nucleus. The heaviest naturally occurring element is Uranium, with an atomic number of 92. The major difference between hydrogen and uranium is the number of protons in their nuclei. The heaviest human-made element is atomic number 118, UUo, known as Ununoctium (from its atomic number “one” “one” “oct,” or eight.). UUo’s discovery (or creation) was announced on October 9, 2006, as a result of collisions between californium-249 atoms and calcium-48 ions. It is believed to be a semi-conducting noble gas.

The Periodic Table consists of rows and columns. The rows are called Periods and denote energy levels of the elements’ outermost electrons. For instance, both hydrogen and helium have their outermost (and only) electrons in the first energy level, which is why they are in the first row the Periodic Table. The second row elements lithium, beryllium, boron, carbon, nitrogen, oxygen, fluorine and neon, each have their outermost electrons in the second energy level, and so on. This is a general rule for each element in a row, but there are notable exceptions which will be discussed later.

The columns are called Groups or Chemical Families. All elements in a a given column or group share similar chemical properties. All the elements in the far-right column are the Noble Gases. These gases generally do not react with other elements.

periodic-table-large

(image: https://upload.wikimedia.org/wikipedia/commons/3/38/R20.png0

There are two general classifications to know about the elements on the Periodic Table, before diving in and looking at individual groups of elements. These two classifications are Metals vs. Non-Metals, and Representative elements vs. Transition elements.

Metals vs. Non-Metals. Most of the elements on the Periodic Table are metals. Metals begin on the left-hand side of the table, and extend all the way to the right, until the stair-step line. To the right of the stair-step line are the non-metals, far fewer in number. Along the stair-step line are the semi-metals, also known as metalloids. The semi-metals are Boron (atomic number 5), Silicon (14), Germanium (32), Arsenic (33), Antimony (51), Tellurium (52) and Polonium (84).

Representative Elements. The representative elements are groups 1-2, and 13-18.

Transition Elements. The groups in-between, 3-12, and the ones down below the table consist of the transition elements. The transition elements can also be broken into two sections. Groups 3-12 are referred to as the transition metals, and the two rows of elements below the main table (atomic numbers 58-71 and 90-103) are the inner transition metals. The first row of the inner transition metals (atomic numbers 58-71) are known as the Lanthanides, because their first element is Lanthanum, and the second row (atomic numbers 90-103) are called the Actinides, because their first element is Actinium. The names are a little deceptive because, depending on the Periodic Table you’re looking at, the elements actinium and lanthanum themselves are often placed among the transition metals, not the inner metals.

 

History of the Periodic Table

The Greeks were the first to float the idea that matter was composed of elements. Aristotle believed these elements to be Earth, Fire, Air and Water, whilst Democritus theorized an atomic theory of matter — that all matter was composed of indivisible units or “atomos.” (”Atomos” means indivisible). Antonie Lavoisier in the 1700s was the first to write an extensive list identifying 33 elements, and distinguishing between metals and non-metals, and John Dalton developed his atomic theory around the year 1800.

As far as sorting these elements into some form of table, Dmitri Mendeleev, though given full credit, was not the first (and not the last). In the 1820s, Jons Jakob Berzelius created a table of elements sorted by their atomic weights, and he replaced the Greek symbols for the elements with English abbreviations.

Johann Wolfgang Döbereiner noted that elements could be arranged into triads according to their physical properties, with the middle element of the triad exhibiting properties in-between the outer two elements. For example, he noted that the atomic weight of the middle element was the average of the atomic weights of the outer two elements. An example of such a triad is lithium, sodium and potassium, three of what we know call the “alkali metals.”

Stanislao Cannizaro determined atomic weights for the elements that were already known in the 1860s, and a table of these elements was arranged by Newlands, beginning with hydrogen. J.A.R. Newlands identified a “Law of Octaves,” in which “the eighth element, starting from a given one, is a kind of repetition of the first.”

Alexandre-Émile Béguyer de Chancourtois turned these atomic masses and repeating properties into a three-dimensional system on a cylinder, which he called the vis Tellurique. In this way,, the known elements were placed in unbroken order of increasing atomic mass.

In 1869, both Dmitri Mendeleev and Lothar Meyer developed periodic tables. The Russian Mendeleev was a chemistry teacher who arranged the periodic table according to increasing atomic mass. His greatest contribution was not the table itself, however, but his recognition of the periodicity of chemical properties, called The Periodic Law, which states that, “if all the elements be arranged in order of their atomic weights a periodic repetition of properties is obtained.” All the more so, Mendeleev’s Periodic Table left gaps for elements that had not yet been discovered, whose properties could be predicted by their placement within the table. When these elements were ultimately discovered, they fit neatly into those gaps, and matched the chemical properties predicted for them.

The Periodic Table has changed much since Mendeleev’s output, but the Periodic Law remains. Firstly, the Noble Gases had not been identified in Mendeleev’s time, so he could not predict their existence. Between the years of 1894 and 1898, Sir William Ramsay discovered five noble gases, and placed them in their own group on the right column of the Periodic Table.

Then, after Henry Moseley was able to identify the atomic numbers of elements using x-ray diffraction data, the Periodic Table of the Elements was reordered in terms of atomic number, not atomic mass.

When Glenn Seaborg discovered some heavier transuranium elements, he placed them at the bottom of our Modern Periodic Table, giving way to the Actinides series of the inner transition metals.