how to find the number of electrons

A. Atomic Number Equals Electrons or Protons
Each element has an atomic number. The atomic numbers are listed along with the names and symbols of the elements on the inside cover of the text. The atomic number equals the charge on the nucleus. It therefore also equals the number of protons in the nucleus and also equals numerically the number of electrons in the neutral atom. The atomic number has the symbol Z.

Different elements have different atomic numbers; therefore, atoms of different elements contain different numbers of protons (and electrons). Oxygen has the atomic number 8; its atoms contain 8 protons and 8 electrons. Uranium has the atomic number 92; its atoms contain 92 protons and 92 electrons.

The relationship between atomic number and the number of protons or electrons can be stated as follows:

Atomic number	= number of protons per atom
	= number of electrons per neutral atom

B. Mass Number Equals Protons plus Neutrons
Each atom also has a mass number, denoted by the symbol A. The mass number of an atom is equal to the number of protons plus the number of neutrons that it contains. In other words, the number of neutrons in any atom is its mass number minus its atomic number.

Number of neutrons = mass number - atomic number
or
Mass number = number of protons + number of neutrons

The atomic number and the mass number of an atom of an element can be shown by writing, in front of the symbol of the element, the mass number as a superscript and the atomic number as a subscript:

mass number
atomic number

Symbol of element

A
Z

For example, an atom of gold (symbol Au), with an atomic number 79 and mass number of 196 is denoted as:

C. Isotopes
Although all atoms of a given element must have the same atomic number, they need not all have the same mass number. For example, some atoms of carbon (atomic number 6) have a mass number of 12, others have a mass number of 13, and still others have a mass number of 14. These different kinds of the same element are called isotopes. Isotopes are atoms that have the same atomic number (and are therefore of the same element) but different mass numbers. The composition of atoms of the naturally occurring isotopes of carbon are shown in Table 4.2.

TABLE 4.2 The naturally occurring isotopes of carbon

Isotope

Protons

Electrons

Neutrons

12
6

13
6

14
6

The various isotopes of an element can be designated by using superscripts and subscripts to show the mass number and the atomic number. They can also be identified by the name of the element with the mass number of the particular isotope. For example, as an alternative to

12
6

13
6

and

14
6

we can write carbon-12, carbon-13, and carbon-14.

About 350 isotopes occur naturally on Earth, and another 1500 have been produced artificially. The isotopes of a given element are by no means equally abundant. For example, 98.89% of all carbon occurring in nature is carbon-12, 1.11% is carbon-13, and only a trace is carbon-14. Some elements have only one naturally occurring isotope. Table 4.3 lists the naturally occurring isotopes of several common elements, along with their relative abundance.

TABLE 4.3 Relative abundance of naturally occurring isotopes of several elements

Isotope	Abundance (%)

hydrogen-1	99.985
hydrogen-2	0.015
hydrogen-3	trace

carbon-12	98.89
carbon-13	1.11
carbon-14	trace

nitrogen-14	99.63
nitrogen-15	0.37

oxygen-16	99.76
oxygen-17	0.037
oxygen-18	0.204

Isotope	Abundance (%)

silicon-28	92.21
silicon-29	4.70

silicon-30	3.09
chlorine-35	75.53
chlorine-37	24.47

phosphorus-31	100

iron-54	5.82
iron-56	96.66
iron-57	2.19
iron-58	0.33

aluminum-27	100

D. The Inner Structure of the Atom
So far, we have discussed electrons, protons, and neutrons and ways to determine how many of each a particular atom contains. The question remains: Are these particles randomly distributed inside the atom like blueberries in a muffin, or does an atom have some organized inner structure? At the beginning of the twentieth century, scientists were trying to answer this question. Various theories had been proposed, but none had been verified by experiment. In our discussion of the history of science, we suggested that, at various points in its development, science has marked time until someone performed a key experiment that provided new insights. In the history of the study of atoms, a key experiment was performed in 1911 by Ernest Rutherford and his colleagues.

1. Forces between bodies
Our understanding of the conclusions drawn from Rutherford's experiment depends on a knowledge of the forces acting between bodies. Therefore, before discussing his experiment, a brief review of these forces is in order. First is the force of gravity that exists between all bodies. Its magnitude depends on the respective masses and on the distance between the centers of gravity of the two interacting bodies. You are familiar with gravity; it acts to keep your feet on the ground and the moon in orbit. Electrical forces also exist between charged particles. The magnitude of the electrical force between two charged bodies depends on the charge on each body and on the distance between their centers. If the charges are of the same sign (either positive or negative), the bodies repel each other; if the charges are of opposite sign, the bodies attract each other. Magnetic forces, a third type, are similar to electrical forces. Each magnet has two poles - a north pole and a south pole. When two magnets are brought together, a repulsive force exists between the like poles and an attractive force between the unlike poles. The magnetic and electrical forces can interact in the charged body. These three forces were known at the end of the nineteenth century when the structure of the atom came under intensive study.

2. Rutherford's experiment
Let us describe Rutherford's experiment, In 1911, it was generally accepted that the atom contained electrons and protons but that they were probably not arranged in any set pattern. Rutherford wished to establish whether a pattern existed. He hoped to gain this information by studying how the protons in the atom deflected the path of another charged particle shot through the atom. For his second particle, he chose alpha () particles. An alpha particle contains two protons and two neutrons, giving it a relative mass of 4 amu and a charge of +2. An alpha particle is sufficiently close in mass and charge to a proton that its path would be changed if it passed close to the proton. In the experiment, a beam of alpha particles was directed at a piece of gold foil, so thin as to be translucent and, more importantly for Rutherford, only a few atoms thick. The foil was surrounded by a zinc sulfide screen that flashed each time it was struck by an alpha particle. By plotting the location of the flashes, it would be possible to determine how the path of the alpha particles through the atom was changed by the protons in the atom. The three paths shown in Figure 4.2 (paths A, B, and C) are representative of those observed. Most of the alpha particles followed path A; they passed directly through the foil as though it were not there. Some were deflected slightly from their original path, as in path B; and an even smaller number bounced back from the foil as though they had hit a solid wall (path C).

FIGURE 4.2 (a) Cross-section of Rutherford's apparatus.

Picture 4.2b

FIGURE 4.2 (b) Enlarged cross-section of the gold foil in the apparatus, showing the deflection of alpha particles by the nuclei of the gold atoms.

Although you may be surprised that any alpha particles passed through the gold foil, Rutherford was not. He had expected that many would pass straight through (path A). He had also expected that, due to the presence in the atom of positively charged protons, some alpha particles would follow a slightly deflected path (path B). The fact that some alpha particles bounced back (path C) is what astounded Rutherford and his co-workers. Path C suggested that the particles had smashed into a region of dense mass and had bounced back. To use Rutherford's analogy, the possibility of such a bounce was as unlikely as a cannonball bouncing off a piece of tissue paper.

3. Results of the experiment
Careful consideration of the results and particularly of path C convinced Rutherford (and the scientific community) that an atom contains a very small, dense nucleus and a large amount of extranuclear space. According to Rutherford's theory, the nucleus of an atom contains all the mass of the atom and therefore all the protons. The protons give the nucleus a positive charge. Because like charges repel each other, positively charged alpha particles passing close to the nucleus are deflected (path B). The nucleus, containing all the protons and neutrons, is more massive than an alpha particle; therefore, an alpha particle striking the nucleus of a gold atom bounces back from the collision, as did those following path C.

Outside the nucleus, in the relatively enormous extranuclear space of the atom, are the tiny electrons. Because electrons are so small relative to the space they occupy, the extranuclear space of the atom is essentially empty. In Rutherford's experiment, alpha particles encountering this part of the atoms in the gold foil passed through the foil undeflected (path A).

If the nucleus contains virtually all the mass of the atom, it must be extremely dense. Its diameter is about 10^-12 cm, about 1/10,000 that of the whole atom. Given this model, if the nucleus were the size of a marble, the atom with its extranuclear electrons would be 300 m in diameter. If a marble had the same density as the nucleus of an atom, it would weigh 3.3 X 10¹⁰ kg.

This model of the nucleus requires the introduction of a force other than those discussed earlier, one that will allow the protons, with their mutually repelling positive charges, to be packed close together in the nucleus, separated only by the uncharged neutrons. These nuclear forces seem to depend on interactions between protons and neutrons. Some are weak and some are very strong. Together they hold the nucleus together, but they are not yet understood.

The model of the atom based on Rutherford's work is, of course, no more than a model; we cannot see these subatomic particles or their arrangement within the atom. However, this model does give us a way of thinking about the atom that coincides with observations made about its properties. We can now determine not only what subatomic particles a particular atom contains but also whether or not they are in its nucleus. For example, an atom of carbon-12

contains 6 protons and 6 neutrons in its nucleus and 6 electrons outside the nucleus.

We have two distinct parts of an atom - the nucleus and the extranuclear space. The nucleus of an atom does not play any role in chemical reactions, but it does participate in radioactive reactions. (Such reactions are discussed later in this chapter.) The chemistry of an atom depends on its electrons - how many there are and how they are arranged in the extranuclear space.

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