Term Paper on Elements | Chemistry

In this term paper we will discuss about the genesis and abundance of elements. 

Term Paper # 1. Genesis of the Elements:

The origin of the elements must be traced back to the origin of the universe itself. The Big Bang theory seems to be the most dominant one in this regard. According to this theory, the entire matter and energy of the universe was cumulated in the form of a cosmic egg of very high density (~10⁹⁶ g cm^–3) and temperature (10³² K). It is not clear how this nucleus was formed. Perhaps the “matter” present in it was actually in the form of radiations. Now, a tremendous and sudden explosion (big bang) occurred approximately 1.8 x 10¹⁰ years ago.

The universe started to expand after this explosion and the temperature began to fall very rapidly. For example, after one second of the explosion, the temperature is supposed to have fallen to ~10¹⁰ K. From this stage onward, the universe was densely populated by elementary particles like neutrons, protons and electrons. During the next 10 – 500 seconds, these particles started to condense, like nuclear fusion reactions, into the nuclei of different elements.

The hot Big Bang theory is supported by the existence of 2.7 K radiation, experimentally verified in 1965 (Penzias and Wilson; Nobel Prize 1978 for this discovery). The universe must have been filled initially with radiation corresponding to its very high temperature, ~10¹⁰ K. As the universe expanded, its temperature came down. It has been estimated that after 1.8 x 10¹⁰ years, the temperature of the universe should be around 3K.

In 1965, Penzias and Wilson built a highly sensitive horn-shaped radio-receiver for use in a space program. While testing it, they discovered a faint whisper of radio noise coming from all directions in outer space. This was actually a microwave radiation of wavelength 1.285 cm. This wavelength corresponds to isotropic thermal black body radiation at a temperature of 2.7 K. Hence, the cosmic microwave back­ground radiation can be considered as a remnant of the Big Bang.

Whatever be the origin of the universe in its earliest form, our knowledge about the forma­tion of the elements is more compact in terms of series of several thermonuclear reactions. The distribution of the various elements throughout the entire universe and their isotopic compo­sitions estimated by wide range spectroscopic studies on the solar system, as well as on stars, galaxies, nebulae and interstellar space can be understood through such schemes of nuclear reactions.

In the process of formation of elements, the initial event appears to have been the formation of neutrons which decayed quickly (half-life = 11.3 min) into electrons, protons and antineutrinos –

After about 1 second, the universe was filled with neutrons, protons, electrons, antineutrino and of course, photons. The temperature was too high to allow the particles to combine—they were present in the plasma state.

As the temperature dropped, the protons could capture electrons to form H atoms. The H atoms could now condense to form mainly helium nuclei. It is estimated that within the first few seconds, ⁴₂He constituted nearly 25 per cent of the mass of the universe. The atoms gathered together to form galactic clusters and then more dense stars. The process of combination of hydrogen nuclei (fusion) continued (hydrogen burning) and huge amount of energy was released in the form of radiation.

Initially the outward thermal pressure counteracted the gravitational force on the gaseous mass, but when approximately 10 per cent of the hydrogen in a star of about the same size as the sun has been used up, the thermal pressure of radiation became insufficient to counteract the gravitational pull. Consequently, the star contracted and the temperature rose higher. When the temperature reached about 10⁸K (100 MK), fusion occurred between helium nuclei forming nuclei of heavier elements (helium burning). Similar processes in large stars gave rise to the nuclei of still heavier elements.

A few representative schemes of such nuclear reactions are summarized below:

Note:

1. ⁴He may also result as the net product from a cycle consisting of C, N and O (Bethe and Weizsacker) –

It has been estimated that about 10% of the energy of the sun comes from this process. Most of the rest comes from the straightforward H-burning.

2. Besides the processes explained above, rapid proton capture by heavier nuclides (^-process) may lead to proton-rich nuclei.

3. Spallation reactions also give rise to some light elements. Cosmic rays consist of a wide variety of atomic particles, from hydrogen to uranium. While travelling great distances in the galaxies, the heavier particles occasionally collide with atoms of the interstellar gas—largely ¹H and ⁴He. As a result, fragmentation occurs and the lighter elements are formed. High speed a-particles may also collide with interstellar iron group elements, inducing spallation. Such processes, together with ¹³C (p, α) ¹⁰B and ¹⁴N (p, α) ¹¹C reactions, followed by β-decay of ¹¹C to ¹¹B, account for the abundance of the lighter isotopes of Li, Be and B.

4. Neutron absorption β emission processes are most significant for the elements beyond iron. The reactions are primarily (n, γ) type, the unstable nuclide formed subsequently undergoing β-decay. In the s-process, neutron capture is slow compared with β-emission while in the r-process, neutron capture is rapid. The nuclides formed by the s-process are controlled by the neutron capture cross section of the precursor nuclide. The stable nuclei corresponding to neutron magic numbers 50, 82 and 126 have very low neutron capture cross sections.

This explains the relatively high abundances of ⁸⁹₃₉Y, ⁹⁰₄₀Zr, ¹³⁸₅₆Ba, ¹⁴⁰₅₈Ce, ²⁰⁸₈₂Pb and ²⁰⁹₈₃Bi. In the r-process, a large number of neutrons are added successively into a single nucleus in a very short time; for example, some 200 neutrons might be added to an iron nucleus in 10-100 s. Eventually the product becomes excessively neutron-rich and a cascade of 8-10 β-emissions result in the formation of a stable nuclide. The abundances of nuclides of mass numbers 80, 130, 194 as well as ³⁶S, ⁴⁶Ca, ⁴⁸Ca are explained in this manner.

Such schemes of proposed nuclear reactions have been considerably developed to account for the observed abundances of different nuclides throughout the universe. Let us now have a glance at the abundances of the elements.

Term Paper # 2. Abundance of the Elements:

The average relative content of an element in any natural system is called its abundance. Spectroscopic analysis of the celestial bodies and analysis of meteorites provide knowledge about the abundance of the elements over the whole universe, or the cosmos; this is often referred to as the cosmic abundance of the elements. Abundances of the elements on the earth are somewhat different and are referred to as the terrestrial abundance of the elements.

I. Cosmic Abundance:

A plot of the abundances of elements (in terms of number of atoms per 10⁶ atoms of silicon) against their atomic numbers is shown in Fig. 1.1. Certain selected values (A. Cameron) are also given in Table 1.1. The values are approximate and disputed. Yet the general features presented by them are interesting:

(i) The abundance data may be clearly divided into two separate curves, one lower and one upper, as shown. The upper curve (solid line, blue) connects the nuclides of even atomic number which are clearly more abundant than the nuclides of neighbouring elements with odd Z (broken line, red).

(ii) Abundances show a rapid exponential decrease from elements of small atomic number to molybdenum (Z = 42). After this, abundances remain more or less constant.

(iii) Hydrogen and helium are most abundant of all elements. Carbon and oxygen come next in the sequence.

(iv) The abundances of lithium, boron (both with odd Z) and also beryllium are unusually low. These nuclides are easily transmuted by nuclear bombardment. Thus ⁸₄Be formed by fusion of two ⁴₂He are readily converted to more stable ¹²₆C (see helium burning reactions).

(v) Nuclides whose mass numbers are multiples of 4 (e.g., ¹⁶O,²⁰Ne, ²⁴Mg, ²⁸Si, ³²S, ³⁶Ar, ⁴⁰Ca, ⁴⁸Ti) are more abundant than their immediate neighbours (rule of Oddo). This shows the stability of the 2-proton-2-neutron combination (“alpha-particle nuclides”).

(vi) Iron (atomic number 26) is marked by a peak in the curve, ⁵⁶Fe being remarkably abundant in comparison to its immediate neighbours (∼10⁴ times). This nuclide has a very high nuclear binding energy.

(vii) Most of the peaks in the curve correspond to magic numbers of protons and neutrons – ⁴₂He, ¹⁶₈O, ⁴⁰₂₀Ca, ⁹⁰₄₀Zr, ¹¹⁹₅₀Sn, ¹³⁸ ₅₆Ba, ²⁰⁸₈₂Pb.

(viii) The most common isotope of a given element is that with an even number of neutrons.

Isotopes containing protons and neutrons in odd numbers are less abundant, e.g., ²₁H, ⁴⁰₁₉K.

Plot of abundances against mass numbers (not shown here) further reveals that – (a) atoms of heavy elements tend to be rich in neutrons; heavy proton-rich nuclides are rare. This lends support to the hypothesis of primordial elemental synthesis by neutron absorption, (b) among the heavier elements, abundance maxima occur in pairs for mass numbers 80, 90; 130, 138; 196, 208. This shows the stability of a magic number of nucleons.

Study of the abundances of elements throws light on the mode of formation of the elements (nucleogenesis) as outlined in the last section. The ultimate abundance of an element depends on several factors, particularly the probability of the nuclear process involved and the stability of the various isotopic species.

The “Rules” of Harkins (1928):

From a close study of the isotopic composition of elements, certain generalizations have been made regarding the stability of a nuclide and its composition.

These may be summarized as follows:

1. No common nucleus except hydrogen contains fewer neutrons than protons.

2. Elements with even number of nuclear charge (or protons) are more abundant and more stable than those with odd charges. They are also richer in isotopes.

3. Nuclei with even numbers of neutrons are more abundant and more stable than nuclei having odd numbers of neutrons.

4. Nuclei with even mass numbers are more abundant than nuclei having odd mass numbers.

The applicability of these generalizations may be readily appreciated with reference to any table of isotopic abundance. The numbers of stable nuclides known for different odd and even combinations of atomic number (Z) and neutron number (N) are also noteworthy .

II. Terrestrial Abundance:

A very small fraction of the mass of the earth is available for direct analysis and study—the crust, the hydrosphere and the atmosphere. They make up less than 1 per cent of the earth by mass. Obviously, indirect methods have to be used to estimate the composition of the earth. One may reasonably assume that the sun and the planets and meteorites of the solar system were derived via the same set of nucleosynthetic events.

Hence the abundance of the non-volatile elements is in the same proportion in the earth as they are in the sun or mete­orites. Related arguments and studies have led to several estimates of the abundances of the elements in the crust of the earth. The estimates differ considerably from one another, but their overall trend is not very different from the cosmic abundance of the elements. Some approx­imate figures are given in Table 1.2.

Certain features of the table are interesting:

(i) Eight elements constitute the major part of the crust—O, Si, Al, Na, Fe, Ca, Mg and K. They make nearly 98.5% of the total.

(ii) Of these eight elements, oxygen is the most predominant. The crust consists almost entirely of oxygen compounds—mainly silicates of the six metals out of these eight elements. In terms of volumes of the atoms, oxygen alone occupies more than 90% of the total volume occupied by the elements. The crust may thus be considered as a packing of oxygen anions— bonded by silicon and the common metals.

(iii) The abundance of certain common elements is much lower than or comparable to those of many less familiar elements; for example (crustal abundances in ppm in parenthesis) –

The abundance of an element in terms of its average percentage in the crust of the earth is expressed in clarke (symbol C). The clarke of oxygen is ∼46, that of silicon ∼28.