Volume 2

What Is an Atom? The Size and Mass of Atoms • Atomic Nuclei and Electrons. Composition and Size of the Nucleus. Protons and Neutrons • Atomic Numbers • Role of Neutrons in the Nucleus. Isotopes • Applications of Isotopes in Chemistry • Atomic Masses, Atomic Weights, and Atomic Mass Units (a.m.u.) Revisited • Exercises

2.2.1. What Is an Atom? The Size and Mass of Atoms. I am not aware of a fully satisfactory official definition of an atom. In the Gold Book, the ultimate authority in chemical nomenclature, the International Union of Pure and Applied Chemistry (IUPAC) defines atom as the "smallest particle still characterizing a chemical element" and a chemical element as a "species of atoms". So, to understand what an atom is, one needs to know what a chemical element is. Yet to understand what a chemical element is, one needs to know what an atom is. Confused?

In this course, we define atoms as uncharged particles that molecules are made up of and that comprise negatively charged electrons surrounding a positively charged nucleus consisting of protons and neutrons.

A molecule is the smallest unit of a substance that retains the composition and chemical properties of that substance.
Digression. It is more accurate to say that a molecule is the smallest unit of a substance that retains most, rather than all, chemical properties of that substance. This amendment to the definition of a molecule is important because more than one molecule of a substance is sometimes required for that substance to exhibit a particular chemical property. For example, one chemical property of water is its ability to react with sodium to give NaOH and hydrogen gas.

2 H2O + 2 Na = 2 NaOH + H2

As is clear from this equation, to exhibit this particular property, two molecules of water are needed. Another example is the dimerization of nitrogen dioxide.

2 NO2 = N2O4

It is clear that this reaction requires two molecules of NO2 to take place.
Atoms are tiny in size. Let us recall Richard Feynman's quote (section 1.2.1), "If an apple was magnified to the size of the Earth, then the atoms in the apple would be approximately the size of the original apple" (Figure 2-6).
Figure 2-6. "If an apple was magnified to the size of the Earth, then the atoms in the apple would be approximately the size of the original apple" (R. Feynman). (source).

To get an idea of the minuscule mass of an atom, picture a standard cardboard box 50 x 50 x 50 cm (Figure 2-7, left) filled up with hard coal anthracite (Figure 2-7, right), which is nearly pure carbon. The mass of the box would then be about 65 kilograms. However, if each carbon atom in the box weighed just 1 g, the box would be roughly as heavy as our entire planet Earth, whose mass is 6 x 1024 kilograms (13 x 1024 pounds).
igure 2-7. A standard 50 x 50 x 50 cm (~20 x 20 x 20") box (left) and anthracite (right; source).

2.2.2. Atomic Nuclei and Electrons. Composition and Size of the Nucleus. Protons and Neutrons. An atom consists of a positively charged nucleus and negatively charged electrons orbiting the nucleus (Figure 2-8). Watch the first 30 seconds of both Videos 2-1 and 2-2 to see two similar animated models of this process.
Figure 2-8. A simple representation of an atom.
Video 2-1. Model: an electron revolving around the nucleus (source).
Video 2-2. Model: an electron revolving around the nucleus (source).

While atoms are microscopic in size, an atomic nucleus is even much smaller, just about 1/100,000th of the size of an atom itself. To get an idea of such a huge size difference, imagine being in the center of the Ericsson Globe Building (Stockholm, Sweden) with a single poppy seed in the palm of your hand (Figure 2-9). The poppy seed is roughly as many times smaller than the Ericsson Globe as the atomic nucleus is smaller than the atom. If you wish to know how it was discovered that atoms contain nuclei that are positively charged, very small, and dense, read about the fascinating Rutherford's Gold Foil Experiment and watch this and this videos.
Figure 2-9. If the nucleus of an atom was enlarged to the size of a poppy seed (about 1 mm or 0.04"; left; source), then the atom would be roughly the size of Stockholm's Ericsson Globe (110 meters or 361 feet in diameter; right; source).

Atomic nuclei consist of particles of two types, protons and neutrons. A proton is positively charged, whereas a neutron is electroneutral (bears no electric charge).

Protons and neutrons have approximately the same mass and are roughly 2,000 times heavier than an electron. In chemical calculations, the mass of electrons in atoms as well as the minute difference between the masses of the proton and neutron are neglected as insignificant.

Table 1 lists the charges and masses of the proton, the neutron, and the electron. What we need to memorize is the charges and the rounded masses of these three particles constituting an atom.

Table 1. Masses and charges of particles constituting an atom.
2.2.3. Atomic Numbers. We already know that species (types) of atoms are called chemical elements. Every element is unique, differing from all other elements by the number of electrons and protons it has. The number of each element in the periodic table, called the atomic number, is the number of electrons an atom of the element has. For instance (Figure 2-10), hydrogen (H) has number 1 in the periodic table, which means that the number of electrons a hydrogen atom has is 1. Carbon (C) is number 6 in the periodic table. Consequently, a carbon atom has 6 electrons. The heaviest naturally occurring element, uranium (U), has number 92, so an atom of uranium possesses 92 electrons.

Since atoms are electroneutral (bear no net electric charge), the number of positively charged protons in the nucleus of an atom always equals the number of negatively charged electrons revolving around the nucleus. Therefore, it is also often said that an atomic number is the number of protons in the nucleus of the atom, or the charge of its nucleus.
Figure 2-10. The atomic number of an element is the number of electrons the atom has, which equals the number of protons the atom has, which equals the charge of the nucleus.

2.2.4. Role of Neutrons in the Nuclei. Isotopes. A positively charged object attracts a negatively charged object. Two negatively charged objects repel, and so do two positively charged objects (Figure 2-11). The attraction and repulsion electric forces are called the Coulomb forces. The shorter the distance between two charges, the stronger the attraction or repulsion, the dependence being quadratic.
Figure 2-11. Two positively charged or two negatively charged objects repel each other, whereas a positively charged object and a negatively charged object attract each other.
Digression. Since negatively charged electrons are located around a positively charged atomic nucleus, how come the electrons do not fall onto the nucleus due to the Coulomb attraction force? Classical physics does not provide a satisfactory answer to this question, but quantum mechanics does. We do not deal with quantum mechanics in our introductory course. If you are interested in learning more, this article might be a good starting point.
Protons are positively charged and therefore repel one another. The role of the non-charged neutrons in an atomic nucleus is to stabilize it by alleviating the proton-proton repulsive interactions. This is illustrated by a simplified model of the nucleus of beryllium (Be), which contains four protons and five neutrons (Figure 2-12).
Figure 2-12. An oversimplified 2-dimensional model of the atomic nucleus of beryllium, Be (atomic number 4) with the positively charged protons drawn in pink and electroneutral neutrons in green.

The number of neutrons in the nucleus of a given chemical element can be different. Such species of the same element varying in the number of neutrons in the nucleus are called isotopes. Even for hydrogen, which has only one proton in the nucleus, three isotopes are known (Figure 2-13). Some isotopes are unstable, constantly undergoing radioactive decay. In our course, we will deal only with stable isotopes.
Figure 2-13. A schematic representation of the three isotopes of hydrogen with the electron orbit drawn in blue, the nucleus in black, the proton in pink, and the neutrons in green.

To specify an isotope using the name of an element, we write the name followed by a hyphen sign and the isotope number, which is the mass of the nucleus ("hyphen notation"). For example, the main isotope of carbon has 6 protons and 6 neutrons in the nucleus. Therefore, the name of this isotope is carbon-12. The much less abundant isotope of carbon, carbon-13, has 7 neutrons in the nucleus, along with (obviously) 6 protons.

An isotope can also be specified using the symbol of an element by writing the atomic mass number (mass of the nucleus) as a superscript before the symbol ("isotope notation"). In this way, the isotopes carbon-12 and carbon-13 are denoted as 12C and 13C, respectively. Likewise, the three isotopes of hydrogen are written as 1H (hydrogen-1), 2H (hydrogen-2), and 3H (hydrogen-3). While 1H and 2H are stable, 3H is radioactive. These three isotopes of hydrogen are so important that each of them has been given a common name and a symbol: protium for 1H (hydrogen-1; symbol H), deuterium for 2H (hydrogen-2; symbol D), and tritium for 3H (hydrogen-3; symbol T). Isotopes of no other elements have common names.

Approximately one-quarter of all chemical elements have only one stable isotope. These elements, called monoisotopic elements, include, among others, 9Be (beryllium-9), 19F (fluorine-19), 23Na (sodium-23), 27Al (aluminum-27), 31P (phosphorus-31), 127I (iodine-127), and 197Au (gold-197).
Digression. Some people immediately think "radioactive hazard" once they hear the word "isotope". There is no reason to be fearful of radioactivity, so long as the isotope is stable, meaning that it is non-radioactive. By eating food and drinking water we consume two isotopes of carbon (12C and 13C), two isotopes of hydrogen (1H and 2H), two isotopes of nitrogen (14N and 15N), and three isotopes of oxygen (16O, 17O, and 18O) on a daily basis. Each time we eat salted foods, we also consume both isotopes of chlorine (35Cl and 37Cl) and the only isotope of sodium (23Na). Radioactive isotopes are a double-edged sword that can cure or kill. Cobalt-60 (60Co) used in cobalt therapy to treat cancer has saved millions of lives. The isotope of fluorine 18F is indispensable for the most sensitive cancer diagnostic tool, positron emission tomography. A nuclear stress test employing radioactive technetium-99 (99Te) is conventionally performed on patients that might have coronary artery disease in order to determine and diminish the risk of a heart attack. On the other hand, it is one of the most dangerous radioactive isotopes, polonium-210 (210Po), that was used in the notorious poisoning of Alexander Litvinenko.
2.2.5. Applications of Isotopes in Chemistry. Do different isotopes of the same element exhibit different chemical properties? Many introductory chemistry texts answer this question negatively. A more honest answer, however, is yes and no. "No" because there is no qualitative difference between different isotopes of a given element in terms of chemical properties. Yet the answer is also "Yes" because some reactions slow down by a factor of 5-6 and even up to 10-13 (at room temperature) upon replacement of the conventional isotope 1H by 2H (deuterium) in certain sites of some reacting molecules. Such cases are rare, though. In most instances, the rates are nearly identical and special methods are needed to detect and measure the minute difference. Such accurate measurements often provide important intimate details of the reaction mechanism, the pathway by which reactants are transformed into products.

Another method to use isotopes for gaining insight into reaction mechanisms is isotopic labeling. This method employs specially synthesized molecules, in which one or more atoms of an element have been replaced ("labeled") by a less common isotope of the same element. The labeled compound is then used for a reaction and the rare isotope is tracked using a detection method. The result might be unexpected and revealing. Here is an example.

Imagine that plain water (H2O) is mixed with specially prepared sulfuric acid that is labeled with deuterium (D2SO4; D = 2H, see above). Some of the water is then distilled off the resultant solution and analyzed by a special method, such as mass spectrometry, to detect the presence of deuterium. The analysis will show that the water in the distillate is a mixture of H2O, D2O, and HOD. We can therefore conclude that the hydrogen atoms of the water and those of the sulfuric acid have interchanged their positions (Figure 2-14). This processes is called H/D exchange or isotope scrambling.
Figure 2-14. Hydrogen (1H) – deuterium (D = 2H) exchange between D2SO4 and H2O.

Note that this exchange reaction is reversible. We have briefly touched on reversible reactions previously, but this is the first time we have used the double arrow symbol "⇄" in place of " = " in a chemical equation or scheme (Figure 2-14). This symbol is conventionally used to indicate reversibility of a chemical transformation.

The H/D exchange between D2SO4 and H2O is not a made-up story. The same result is obtained if H2SO4 and D2O are mixed, and in both cases the 1H and 2H (D) isotopes turn out to be evenly distributed over the molecules of water and sulfuric acid. Without such isotopic labeling experiments, there would have been no way of knowing that H atoms of an acid and water interchange their positions.

Various stable and radioactive isotopes of hydrogen and other elements are used in isotopic labeling investigations. In Volume 4, we will see how the mechanism of esterification, a very important organic reaction, was established by an 18O isotopic labeling experiment.

2.2.6. Atomic Masses, Atomic Weights, and Atomic Mass Units (a.m.u.) Revisited. Atoms are microscopic and their masses are miniscule. Measuring atomic masses in kilograms, pounds or even grams does not make any sense and would be as ridiculous as expressing masses of diamonds in tones. For example, the number of Fe atoms in just one gram of iron exceeds 1022 or, in other words, more than 10 thousand billions of billions. We certainly need a convenient mass unit for masses of atoms and molecules. This unit is a.m.u. (atomic mass unit), also known as the dalton (Da), which is defined as 1/12th of the mass of an atom of the carbon isotope 12C.

Take a minute to review the atomic weights of elements in the periodic table. You will see that all of these numbers are fractional, except for the artificially made elements such as technetium (Tc) and promethium (Pm). Why? Should all atomic weights in the periodic chart not be whole numbers, as long as the mass of a proton = the mass of a neutron = 1 a.m.u.? The answer is No, and the main reason for that is the occurrence of more than one isotope for most of the elements. The atomic weights presented in the periodic chart for naturally occurring elements have been determined experimentally, using various real substances. These experimental methods measure atomic weights as a weighted arithmetic mean of the masses of all of the naturally occurring isotopes, based on their natural abundance. A bit confused? Continue reading.

Let us consider carbon. If there were only one isotope of carbon in nature, 12C, then the atomic weight of carbon would be 12. However, there are two more naturally occurring isotopes of carbon, carbon-13 and carbon-14. While 14C is present in trace quantities and can be neglected in our calculation, the abundance of 13C, approximately 1%, should not be ignored. Per each 99 carbon atoms of 12C there is 1 atom of 13C. The weighted average mass of one carbon atom is therefore [(12 x 99) + (13 x 1)]/100 = 12.01 a.m.u., which is the atomic weight value found in the periodic table.

If you still have a problem understanding this idea, picture a box containing many thousands or even millions or billions of glass beads, blue and red. One blue bead weighs 12 g and one red bead 13 g. Per each 99 blue beads in the mix, there is one red bead (Figure 2-15). The weighted average mass of one bead in the mix equals [(12 x 99) + (13 x 1)]/100 = 12.01 g. Now imagine that each blue bead is a 12C atom whose mass is 12 a.m.u. and each red bead is a 13C atom whose mass is 13 a.m.u.
Figure 2-15. Per each 99 blue beads weighing 12 g each there is one red bead that weighs 13 g.

There are two more contributors to the atomic weights in the periodic table being fractional.

- The masses of protons and neutrons are not exactly 1 a.m.u. (Table 1).

- Mass defect is the small yet detectable difference between the mass of an atomic nucleus and the sum of masses of the protons and neutrons comprising that nucleus. This difference is due to the release of energy upon formation of an atomic nucleus from isolated protons and neutrons, according to Einstein's formula E = mc2.

For the vast majority of areas of chemistry, however, the contribution from these two factors are not significant enough to be taken into account.

In section 2.1 above, we mentioned the three "discrepancies" where an element with a lower atomic number has a higher atomic weight than its neighbor with a higher atomic number (Ar vs. K; Co vs. Ni; and Te vs. I). Now that we are aware of the existence of isotopes, we should be able to see that there is no discrepancy there. It is all about the number of neutrons in the nuclei of naturally occurring isotopes within each of the Ar-K, Co-Ni, and Te-I pairs. The most abundant isotope of argon (40Ar, >99%) is heavier than the most abundant isotope of potassium (39K, >93%). Although a potassium atom is one proton heavier than an argon atom, the natural isotopes of argon beat those of potassium in terms of the number of neutrons. This is also the case with the Co-Ni and Te-I pairs.

Guessing how many isotopes an element has on the basis of its atomic weight specified in the periodic table is useless. For instance, one might have thought that bromine (Br) is a monoisotopic element, 80Br, because its atomic weight (79.9) is just 0.1 a.m.u. short of 80. This is not the case however, as 80Br is actually not a natural stable isotope. The naturally occurring isotopes of bromine are 79Br and 81Br, existing in a roughly 1:1 ratio, which makes the average approximately 80. Likewise, the atomic weight of tin (118.71) says nothing about its isotopic composition. In fact, tin is the element with the greatest number of stable isotopes (ten!), their abundance ranging from ~0.3% for 115Sn to ~32.6% for 120Sn.

Perhaps you do not like my use of the terms "atomic mass" and "atomic weight" interchangeably. In physics, mass and weight mean two different things: mass is the quantity of matter, whereas weight is the gravity force acting on an object. In chemistry however, both mass and weight mean the same thing, the quantity of matter. It is noteworthy that while "mass" is more frequently applied to a single isotope of an atom, "weight" is conventionally used for the average mass of all of the naturally-occurring isotopes of a given element.

2.2.7. Exercises.

1. An atom is (a) much bigger in size than its nucleus; (b) comparable in size with its nucleus; (c) slightly bigger in size than its nucleus. Answer

2. It is sometimes said that matter is largely made of emptiness. Why? Answer

3. An atomic nucleus consists of (a) positively charged protons and negatively charged electrons; (b) positively charged protons, electroneutral neutrons, and negatively charged electrons; (c) positively charged protons and electroneutral neutrons; (d) uncharged neutrons and negatively charged electrons. Answer

4. The atomic number of an element is (a) the number of electrons an atom of that element has; (b) the number of protons an atom of that element has; (c) the number of protons and neutrons an atom of that element has; (d) the charge of the atomic nucleus; (e) the number of protons minus the number of neutrons in the nucleus of an atom of that element. Answer

5. The nucleus of an element consists of 15 protons and 16 neutrons. What element is that? What is the isotope? Is this element monoisotopic? Answer

6. A neutron is (a) slightly heavier than a proton and much heavier than an electron; (b) heavier than electron but much lighter than a proton; (c) much heavier than a proton but lighter than an electron; (d) lighter than a proton and an electron. Answer

7. Different isotopes of the same element have identical chemical poroperties. True or false? Answer

8. Find fluorine in the periodic table. Fluorine is a monoisotopic element. How many protons, neutrons, and electrons does a naturally occurring fluorine atom have? Answer

9. Why is the atomic weight of argon (atomic number: 18) higher than that of potassium (atomic number:19)? [Answer: See section 2.2.6]

10. Magnesium (Mg, atomic #12) has three naturally occurring stable isotopes: 24Mg (79%), 25Mg (10%), and 26Mg (11%). How many protons and neutrons does each of these isotopes have? Using the isotopic distribution percentages, calculate the atomic weight of naturally occurring magnesium. Answer