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Allotropes of an element are different and separate from the term isotope and should not be confused. Some chemical elements can form more than one type of structural lattice, these different structural lattices are known as allotropes. This is the case for phosphorus as shown in Figure 2.9. White or yellow phosphorus forms when four phosphorus atoms align in a tetrahedral conformation (Fig 2.9). The other crystal lattices of phosphorus are more complex and can be formed by exposing phosphorus to different temperatures and pressures. For example, the cage-like lattice of red phosphorus can be formed by heating white phosphorus over 280oC (Fig 2.9). Note that allotropic changes affect how the atoms of the element interact with one another to form a 3-dimensional structure. They do not alter the sample with regard to the atomic isotope forms that are present, and DO NOT alter or affect the atomic mass (A) of the element.

Figure 2.9 Allotropes of Phosphorus. (A) White phosphorus exists as a (B) tetrahedral form of phosphorus, whereas (C) red phosphorus has a more (D) cage-like crystal lattice. (E) The different elemental forms of phosphorus can be created by treating samples of white phosphorus with increasing temperature and pressure.
Source: https://en.wikipedia.org/wiki/Allotropes_of_phosphorus
Different allotropes of different elements can have different physical and chemical properties and are thus, still important to consider. For example, oxygen has two different allotropes with the dominant allotrope being the diatomic form of oxygen, O2. However, oxygen can also exist as O3, ozone. In the lower atmosphere, ozone is produced as a by-product in automobile exhaust, and other industrial processes where it contributes to pollution. It has a very pungent smell and is a very powerful oxidant. It can cause damage to mucous membranes and respiratory tissues in animals. Exposure to ozone has been linked to premature death, asthma, bronchitis, heart attacks and other cardiopulmonary diseases. In the upper atmosphere, it is created by natural electrical discharges and exists at very low concentrations. The presence of ozone in the upper atmosphere is critically important as it intercepts very damaging ultraviolet radiation from the sun, preventing it from reaching the Earth’s surface. Thus, ozone can be a health hazard or a health protector, depending upon where it is found!
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2.8 Electronic Structure of Atoms

Although we have discussed the general arrangement of subatomic particles in atoms, we have said little about how electrons occupy the space about the nucleus. Do they move around the nucleus at random, or do they exist in some ordered arrangement?
The modern theory of electron behavior is predicted by the field of quantum mechanics. The term quantum is defined as a discrete quantity or ‘packet’ of energy. For example, light has qualities of both a wave and a particle. Since it has properties of a particle, the energy of light is said to be quantized into discrete ‘packets’ of light particles called photons. Each photon of light, then carries a quantized amount of energy that is dependent on its frequency.
Electrons in atoms are also quantized and can exist at different energy levels depending on how far away from the nucleus of that atom that they are positioned. This is of interest, because the electrons are the mobile part of the atom and they are involved in forming chemical bonds. Understanding their positioning around the nucleus of the atom helps to predict how they will combine with other atoms to form chemical compounds. Electrons typically have higher energy, the farther away they are (on average) from the nucleus. However, the increasing energy of an electron does not proceed continuously like a ramp the farther away from the nucleus that it travels. Instead, the energy of an electron is quantized, meaning that the energy of an electron does not increase continuously, but instead increases by levels adding discrete packets of energy. This would be similar to walking up a staircase rather than a ramp. On a staircase, you can step up one step at a time, or maybe two steps at a time, but you can never step up a half of a step. Similarly, electrons travel between energy levels instantly, never having an energy amount in between two levels.
A total of four quantum numbers are used to describe completely the movement and trajectories of each electron within an atom. According to the Pauli Exclusion Principle, no two electrons can share the same combination of four quantum numbers. Thus, each electron in an atom has a unique set of quantum numbers that helps define the probable location of an electron within an atom. The quantum numbers that help to define electron location exist in a hierarchical order. This would be very similar to finding an address of a friend. If you don’t know your friend very well, you may only know the city where your friend lives. This doesn’t provide very much information. As you get to know them better, you may find out what neighborhood in the city that they live in. At a deeper level, you may find our what street they live on, and then at the deepest level, what their house number is on that street. However, knowing which house your friend lives in does not tell you where in the house you friend is at, maybe they are in the kitchen or the backyard. Determining the exact location of an electron is not possible. We can only find the approximate location or “address” of the electron.

The Four Electronic Quantum Numbers

There are a total of four quantum numbers: the principal quantum number (n), the orbital angular momentum quantum number (l), the magnetic quantum number (ml), and the electron spin quantum number (ms) that are used to describe the major characteristics and spatial distribution of electrons within an atom. The quantum numbers correspond to the following hierarchical layers: the principle quantum number (n) is the broadest classification and corresponds to the energy shell (this would be equivalent to the city in our address analogy), the orbital angular momentum quantum number (l) is the next layer and corresponds to the subshells (this would be the neighborhood in our address analogy), the magnetic quantum number (ml) corresponds to the electron orbitals (or the street where your friend lives), and electron spin quantum number (ms) defines the spins of electrons (or the house number in our address analogy).

n = shell

l = subshell

ml = orbital

ms = electron spin

 
The principal quantum number, n, designates the electron shell. Because n describes the most probable distance of the electrons from the nucleus, the larger the number n is, the farther the electron is from the nucleus and the larger the atom. The principal quantum number (n) can be any positive integer between 1 and 7. An n=1 designates the first principal shell (the innermost shell). The first principal shell is also called the ground state, or lowest energy state. When an electron is in an excited state or gains energy, it may jump to the second principle shell, where n=2. This process is called absorption because the electron is “absorbing” photons, or gaining energy. Thus, as the energy of the electron increases during absorption, so does the principal quantum number, e.g., if an electron in the n = 3 shell absorbs energy, it will jump to the fourth principal shell, n = 4. The opposite process is emission, where electrons “emit” or release energy as they fall from higher to lower principle shells. In this case, n decreases by whole numbers (packets or quanta of energy). Within atoms there is a maximum number of seven electron shells (n = 7), after which the atom becomes too unstable to hold electrons in place.
At a basic level, the energy shells can be thought of like the layering of an onion, with the first layer being the smallest and closest to the core of the nucleus, and the subsequent layers being larger and farther away from the core. Larger shells have more space and can hold more electrons. The general formula for determining how many electrons can be housed in each shell is 2n2 and is shown in Table 2.4. While this table predicts that that outer shells, which are the largest shells can contain 50, 72, and 98 electrons, elements that have this many electrons in those shells have never been discovered. It is likely that they are too big and unstable to exist.

Table 2.4 Maximum Number of Electrons Per Shell

The periodic table allows us to easily determine how many protons (and therefore electrons) an element will have by showing the atomic number (Z) in each element box. Equally useful, the periodic table is set up to represent the different quantum numbers to facilitate the determination of electron configuration of an element. The principle quantum number (n) or number of shells present in an element are shown in the periods or rows of the periodic table (Figure 2.10). For example, if we look at the sodium atom, we will see that it is in row 3 of the periodic table. This means that it has three electron shells that can house electrons. As electrons fill their available orbital spaces, they always fill the shells starting at the lowest energy levels and going up to higher levels as needed. This rule can be formally noted as the Aufbau principle which states that electrons orbiting one or more atoms will fill the lowest available energy levels before filling higher energy levels.
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