Elemental Isotopes and Allotropes Essay Paper

Physical Science

Elemental Isotopes and Allotropes

The 19th century discovery of the periodic table of the elements by Dmitri Mendeleev gave an organizing principle to understanding the structure of the atom, and deriving atomic weight. On the periodic table, the lighter elements have atomic weights which correspond to whole numbers. Hydrogen has an atomic weight of 1, which corresponds to the idea that it has only one proton (and the weight of an electron is statistically insignificant in this measurement). But moving further along the periodic table, it became clear that the numbers eventually became less predictable. In the 19th century Dalton had suggested further atomic weights were simply multiples of hydrogen, which to a certain degree matched the available evidence.

But it was the discovery of the neutron in 1932 that actually yielded the correct answer. Rutherford had hypothesized the existence of an extra particle in the nucleus that did not bear a charge, but that bore the equivalent weight of a proton, terming it the “neutron,” in 1920. Chlorine’s atomic weight on the periodic table is given as 35.45, which seems to disprove Dalton’s hypothesis, as this could not be construed as an even multiple of the weight of hydrogen. The notion that there was an extra particle in the chlorine atom now led to the question of how the uneven atomic weight was possible — the solution is that chlorine additionally exists in two separate isotopes, or naturally occurring atomic forms. Chlorine-35 has an atomic weight of 34.97, and contains 17 protons and 18 neutrons. The heavier Chlorine 37 has an atomic weight of 36.97, and contains 2 additional neutrons.

As a result the atomic weight of Chlorine is calculated from determining the average occurrence of its two major isotopes. Through analysis it is revealed that roughly 3 out of 4 Chlorine atoms are of the lighter isotope (76%). As a result, the calculation may be done as follows:

.76 (34.97) + .24 (36.97) = 35.45

In other words, the percentage of the particular isotope multiplied by its atomic weight, when added to similar figures for other isotopes, yields a sum that is equivalent to the atomic weight as stated on the periodic table.

Isotopes, in which the individual atom has a separate atomic weight, should be distinguished from allotropes, which are competing forms that can be taken by the same element in its pure state. The best example of this is carbon: we are familiar with the ability of polyvalent carbon to link with itself in very different ways, as witnessed by the softness of elemental carbon in graphite, and the hardness of elemental carbon in diamonds. In this particular case, it is illustrative to note that new forms are still being discovered: Blundell gives a good account of the discovery in 1985 of a new form of carbon, in which Sir Harry Kroto and a team in Houston, Texas “identified a species containing sixty carbon atoms” and eventually determined that “the only geometric shape that could combine sixty carbon atoms into some sort of spherical structure was a set of interlocking hexagons and pentagons, exactly as is found on some soccer balls.” (Blundell 112). The corresponding molecule, known as a “buckyball” or by the scientific name buckminsterfullerene due to its similarity to the geodesic domes of Buckminster Fuller, has become important as pointing the way forward for nanotechnological engineering conducted on the molecular level.

Electrolysis of Water

Electrolysis of water is the simplest way of demonstrating the effects of electrical activity on the molecular level. Electrolysis is the means of provoking a chemical reaction that would not otherwise take place by supplying the activation energy required for the reaction with the means of an electrical current. Water of course has a chemical formula of H2O, however H2O itself is a poor conductor of electricity unless it contains some kind of positive and negative ions. For the purposes of demonstrating electrolysis, the use of tap water is suitable; otherwise the water requires some form of salt dissolved in it. When electric currents move electrical energy through the liquid, this requires the presence of ions in the liquid to carry the charge. In electrolysis, both positive and negative ions are required: this is the basic state of ordinary tap water, for example.

The basic formula for the chemical reaction that occurs is as follows:

2H2O 2H2 + O2

Calculating the potential for this reaction yields a negative result, which is why the addition of energy from an outside source is required to begin it. As a result, the application of electric current to the liquid water results in the production of two separate elemental gases, hydrogen (H2) and oxygen (O2). Mortimer notes that the full chemical reaction occurs in two half-reactions: “this process is called a half-reaction because it cannot take place unless another process accepts the electrons that are produced.” (355).What needs to be done is to permit the water to conduct the current, so a battery is connected to an anode and cathode that will facilitate the reaction (generally platinum). The positively charged anode attracts additional loose electrons, and is able to facilitate an oxidation reaction, in which the water decomposes to gaseous oxygen and dissolved hydrogen ions. The negatively charged cathode causes a reduction reaction by contrast, in which the hydrogen gas is produced. The equation predicts that hydrogen should be produced in precisely twice the amount as oxygen, which can be measured depending upon how the apparatus is designed.

Quantum Entanglement

Quantum entanglement is a concept in atomic structure, following the 20th century quantum theory of the atom. It is noteworthy for providing an instance where Albert Einstein offered what he thought was a hypothetical disproof of the quantum theory, which to a certain extent he distrusted — but Einsein’s objections, which involved the notion of quantum entanglement, have been shown in experiments to have been incorrect.

Einstein believed that quantum mechanics was incomplete as a description of the universe, and together with two co-authors offered the Einsten-Podolsky-Rosen paradox in 1935 as a way of describing what Einstein saw as the incompleteness of quantum theory. The standard “Copenhagen” interpretation of quantum theory held that if the position of an electron was measured then its momentum could not be precisely known, and that if its momentum was known then its position could not be measured. Einstein’s famous remark “God does not play dice with the universe” was intended as a critique of the radical uncertainty this gives to the actual physical existence of the electron (the “local realism” theory, to which Einstein was inclined).

In consequence Einstein Podolsky and Rosen proposed a hypothetical experiment that showed an apparent paradox in the quantum theory itself. Assuming an event in which two electrons are emitted simultaneously and collide. Their collision must observe Newton’s third law, so therefore if the momentum of one is measured and the location of the other is measured (which is possible according to quantum mechanics) then the values for momentum and location for both particles can both be known. The response of quantum theory was that if this was the case, then what would have to go was Einstein’s “local realism.” But in this case, that meant that one electron might change state when the other was measured: Einstein thought that, in this case, the quantum theory was predicting what he famously called “spukhafte fernwirkung,” or “spooky action at a distance.” How could two electrons separated by space “know” what was happening?

The mathematics of the problem were originally solved in the 1960s by the Irish physicist John Bell, establishing the concept known as “Bell’s Inequality.” Bell’s mathematical predictions revealed that, under the right circumstances, this “spooky action at a distance” — or “quantum entanglement,” to give the term that Schrodinger (who first described it as a possibility) used — would indeed prove to be the case, contrary to Einstein’s beliefs. The set-up of Bell’s experiment is given in the diagram:

Polkinghorne outlines Bell’s explanation of the EPR paradox as follows:

He analysed what properties the 1 — 2 system would have if it were a genuinely separated system (as Einstein had supposed), with properties at 1 depending only on what happened locally at 1 and properties at 2 depending only on what happened locally at 2. Bell showed that if this strict locality were the case, there would be certain relations between measurable quantities (they are now called the Bell inequalities) that quantum mechanics predicted would be violated in certain circumstances. (Polkinghorne 79).

It was not until about 20 years later that Bell’s theories could be confirmed by experiemental observation, but it was discovered that indeed Bell was right and Einstein was wrong. “Spooky action at a distance” does appear to be the case in quantum entanglement, and leads to the phenomenon known informally as “quantum telepathy.” As Marcus Chown says, alluding to this description, “entangled particles behave like a single indivisible entity. At some level, they know each other’s deepest secrets.” (Chown 57).

Works cited

Blundell, Stephen. Superconductivity. Oxford and New York: Oxford University Press, 2009. Print.

Chown, Marcus. The Quantum Zoo. Washington: Joseph Henry, 2006. Print.

Mortimer, Robert G. Physical Chemistry. Third Edition. Amsterdam and Boston: Elsevier Academic Press, 2008. Print.

Polkinghorne, John. Quantum Theory. Oxford and New York: Oxford University Press, 2002. Print.

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