http://t3.gstatic.com/images?q=tbn:ANd9GcQ9nKMKYTeGdCgXl3Uymg-Gg5qHApk9OHalIkwaxxDlD_9L4_eS

 

The Origin of the Earth:

For all accounts, it looks like the Earth was formed about 4.6 billion years ago [1] by accretion from the solar nebula [2]. Accretion means the growth of a massive object by gravitationally attracting more matter, typically gaseous matter in an accretion disk[3]. At this point, all the chemical elements that we find in the Earth were already here because there is no question that new chemical elements could NOT be created in the Earth. What I want to discuss is this point: HOW ALL THESE CHEMICAL ELEMENTS GOT HERE?

Now letís have a look at the chemical structure of the Earth by layers [4]:

a cross-sectional view of Earth showing the layers classified by chemical composition.

The Chemical composition of each of the Earthís Layers is explained here ( taken from [4]):

Inner Core. About 800 miles in diameter and composed of more than 90% iron with a maximum density of 13 g/cm3. This iron in this layer, although very very hot, is solid due to the immense pressure at the center of the Earth.

Outer Core. About 1240 miles thick, the outer core is also made mostly of iron with a density of about 10 g/cm3. However, a reduction in pressure makes this hot layer a liquid.

Mantle. About 1860 miles thick, the mantle is made of iron and magnesium-rich silicate rocks and has a density of about 4.5 g/cm3. The mantle is hot, but mostly solid because the minerals are under pressure.

Asthenosphere. The upper reaches of the mantle are not solid; they are considered plastic and flow very slowly. This is due to the reduction in pressure as we approach the top of the mantle- the rocks are more likely to begin to melt.

Lithosphere. This layer varies in thickness from 1 to 250 miles. The lithosphere is a cool, strong and rigid layer. Its uppermost part is called the crust and is divided into oceanic and continental-type crusts discussed in the next section.

Letís forget about the Lithosphere which is a very small part of the total volume.Most of the rest of the Earth is made of Iron, Nickel, Silicon, and other middle weight elements.Why? My hypothesis is that as a matter of fact, the Earth is the residual of a very old star (ďOur Mother StarĒ) that exploded as a Supernova Type I. As a residual of the explosion, our Earth (and probably other planets like Mercury, Venus and Mars that have about the same density as the Earth) started wandering through the space until they moved close and were attracted by the gravitational field of our Sun.Now, I will argue my point of view.

Something should be quite clear. The internal structure of the Sun, and the internal structure of the Earth are totally different, the chemical composition of the Sun and the Earth are totally different. For example, the internal structure of the Earth is something like this [10].

http://www.windows2universe.org/earth/images/earth_cutbk_sm.jpg

Binding Energy per Nucleon:

First, we will discuss what Nuclear Physics has found about the structure of an atomic nucleus. As we all know, the atom is made of a nucleus and a bunch of electrons outside the nucleus. The nucleus is made of protons and neutrons. Protons and the Neutrons are very similar because they are made of three quarks each. That is why they are generically called NUCLEONS. Each proton is made of two quarks up and one quark down, while each neutron is made of two quarks down, and one quark up. The quarks up have an electric charge of +2/3 of the electron charge e (1.6x10-19 C), while the quark down has an electric charge of -1/3 of the electron electric charge (e). That explains why the proton has electric charge positive (+e), while the neutron has a net electric charge equal zero.

The mass of the electron is about 1800 times smaller than the mass of the nucleons. That means that the mass of an atom is practically determined by the mass of its nucleus. Today we know that the chemical interaction between atoms is determined by the interaction between the electrons in these atoms. But, the number of electrons in a neutral atom is equal to the number of protons in the nucleus. The number of protons in the nucleus is called the ATOMIC NUMBER and is represented by the symbol Z. The number of neutrons in the nucleus is represented by the symbol N and the sum Z + N = A is called the mass number.

The simplest atom we find in nature is the hydrogen, which is made of one proton and one electron. The next simplest atom is the helium. The neutral atom of helium has two electrons, so there should be two protons in the nucleus. But if you try to put to protons in the very small volume of the nucleus, there will be so big electrostatic repulsion between the two protons (because both of them have positive electric charge) that they canít be in peace together. Here is the reason why we need the neutrons. If you put one neutron in contact with the two protons, then they can live together, but if you put two neutrons, it will be even better. That is why the usual atoms of helium (that we use to fill the balloons!), have two neutrons together with the two protons. So the neutrons act like glue keeping the protons together in the nucleus.

The chemical properties of the atoms are determined by the number of protons, but in nature we find atoms with the same number of protons and different number of neutrons. For example most of the atoms of Oxygen in the air have 8 protons and 8 neutrons, but some of them have 9 neutrons, and others have 10 neutrons. Atoms with the same number of protons but different number of neutrons are called ISOTOPES. So O16, O17, O18 are different isotopes of the element Oxygen. From the chemical point of view they are quite similar, but from the physical point of view they are very different. The main difference between isotopes is their stability. Let me explain what we mean by stability.

Letís consider we want to form the nucleus He4. This nucleus has two protons plus two neutrons. The fact is that the mass of the nucleus He4 is smaller than the mass of the two protons plus the mass of the two neutrons. The difference between the mass of the four nucleons and the mass of the nucleus He4 is called the mass defect. The bigger the mass defect, the higher is the stability of the nucleus. Using the relationship between mass and energy found by Einstein ( E= Mc2, where c is the speed of the light in the vacuum), the mass defect can be expressed in terms of energy. That energy associated with the mass defect is called the binding energy of the nucleus and usually is represented by the symbol B. Now, if you divide the binding energy of the nucleus (B), by the number of nucleons in the nucleus (A), you get the so-called, binding energy per nucleon(B/A). Here is a graph showing the binding energy per nucleon[5].

binding enery per nucleon

It is absolutely impossible to overestimate the importance of this graph. This graph explains why we get so much energy from a nuclear explosion. This graph explains how the Sun gets the energy which is so important in our live. This graph also explains the distribution of chemical elements in the Universe.

As you can see in the graph, the nucleus Iron-56 (Fe56) is more stable than the nucleus Uranium-238(U238). That means, if somehow you can transform U238 into Fe56, you will get some excess of energy. That is what happens in a nuclear explosion! Using the same logic, if you can transform hydrogen into helium, again you will get some excess of energy. This is what happens in our Sun! As a matter of fact the same thing happens in millions of other young stars. But, what I want to discuss is the last part: the distribution of chemical elements in the Universe.

Temperature and Energy:

It looks like the idea of the Big Bang works. At least, so far, we have not found any evidence that contradicts it. If this is correct, then 3 minutes after the Big Bang the Universe....Ēconsisted of 22-28 percent helium, with almost all the rest hydrogenĒ [6]. At this point, the temperature of the universe was about 1,000 million degrees Kelvin (109K). Letís talk a little bit about the relationship between temperature and energy. If we have a group of particles (like electrons or nucleons or nuclei) we can associate the temperature with the average energy of each particle. So, the average energy of each particle will be proportional to the temperature.

The common sense tells us that the higher the temperature, the higher the energy of the system. The concept of temperature is usually associated with a big system, a big number of particles. We do not talk about the temperature of an electron, or the temperature of nucleon. So, the temperature is a macroscopic concept. Since the concepts of atoms (or molecules) were proven to be correct, when we talk about the energy of a system, what we mean is the sum of the energy of each of the components of the system. For example: when we burn a mol of gasoline (octane), we get an energy of 5465.6 kJ[7]. What we mean is that for each molecule of octane we get 9.0791x10-18 Joules. If we use the more appropriate unit of energy ev ( 1 electron-volt = 1.6x10-19 J) then the energy we obtain from one molecule is about 56.744 ev. This evidently is a microscopic concept.

It was Ludwig Eduard Botlzmann (1844-1906) the first who established a connection between the macroscopic and the microscopic properties of a system. So, we shouldnít be surprised if we say that to transform the temperature ( measured in Kelvins) into Energy ( in Joules) we multiply the temperature by a constant that is called the Boltzmann constant that we represent by the symbol k and has the value k=1.3806488x10-23 J*K-1. This energy will be kind of an average energy for each particle in the system. For example, at a temperature of 300 K (which corresponds to a temperature of 270C) the product kT = 4.14x10-21 J or 0.0259 ev.

Let me give an example of the relationship between energy and temperature. We know that the ice transform into water a 273 K (0oC). If we multiply this temperature by k, we get about 0.024 ev per molecule. Now, the energy needed to transform 1 kg of ice into water is about 334 kJ. If we calculate the energy needed for one molecule we get ~6.01 kJ/mol, or what is equivalent ~0.0625 ev/molecule. So though the product kT doesnít give us the exact value of the energy available for each particle in the system, it however gives us an idea of the order of magnitude of the energy available. Another example, the metal iron (Fe) melts at about 1500 K, that represents ~0.129 ev per atom. On the other side the iron melting energy is about 272 kJ/kg, that represents ~.16 ev per atom.

In the same way that if the temperature is much bigger than 273 K we donít expect to find ice, if the temperature is much bigger than 1500 K we donít expect to find iron solid.All of this is true assuming that the pressure is the atmospheric one. If the pressure is different this number could change. But, anyway, the temperature will tell us what kind of processes we could expect to have around.

 

From this picture (taken from [8]) we get an idea of the distribution of the temperature inside the Earth.

http://www.hyy.com.cn/images/icon/TemperatureInsideEarth.jpg

From this picture (taken from [9]) we get an idea of the distribution of the temperature inside the Sun

Sundiag.gif (238734 bytes)

 

From these pictures we can see that the temperature close to the center of the Sun is about 15,000,000 K while the temperature close to the center of the Earth is about 5,000K and that means about 3000 times lower.What are the implications of that?

Using the Boltzmann constant we find that the energy associated with the Sunís temperature is about kT = k=1.3806488x10-23 * 15,000,000 = 2.07x10-16 J = 1.29x103 eV, while the energy associated with the Earthís temperature will be around 3000 times smaller or about 0.43 eV. From here we can conclude that some processes could occur inside the Sun, but not inside the Earth. Letís discuss some of these possible processes.

The Sun is full of Hydrogen. In normal conditions the hydrogen atom is made of one proton (nucleus) plus an electron. The binding energy of this electron with the proton is about 15 eV and that means that there is no way the electron could be together with the proton forming the hydrogen atom inside the Sun because this number is much smaller than 1.29x103 eV. The temperature is so high that there will be enough energy for the electron to be free from the proton. On the other side, we know that the density of the Sun is about 1.4x103 kg/m3, which is a little bit more than the density of the water. So the distance between atoms in the Sun should be around 10-10 m like in the water. But the dimension of each proton is about 10-15m, so the distance between two consecutive protons should be around 100,000 times its dimensions. So we can imagine the center of the Sun like a gas of protons colliding with each another. Most of these collisions will be just like the collision of two billiard balls, elastic collisions. Could this happen that because of these collisions two protons could ďpenetrateĒ each another through a nuclear reaction? Letís see:

The radius of a proton [11] is about 0.88Ī0.01x10-15 m. Because all protons have positive charge, when two of them are in contact, there will be an electrostatic Coulomb energy of repulsion of about 1.6x106 ev. That is about 1000 times bigger than the kinetic energy the protons have inside the Sun as we calculated before. You could think that because of this, logically, we should not have a nuclear reaction between the two protons inside the SunÖ. Not true! The reason why is not true is because the rules of quantum mechanics allow a particle with some energy E to traverse a potential barrier higher than E! This effect is known as a ďtunnel effectĒ.

We should be clear that the tunnel effect does not mean that when two protons collide they will create automatically a nuclear reaction. As a matter of fact, most of the collisions will not result in a nuclear reaction.

From the classical point of view, the tunnel effect is a non-sense. It is like hitting a squash ball against the wall and finding the ball on the other side of the wall. Itís impossible we would say! However in the micro-world, the world of atoms, molecules, nuclei and elementary particles, this is quite possible. As a matter of fact there are a lot of examples where the tunnel effect plays a central role. In Nuclear Physics, to explain the Proton and Alpha Decay, in Solid State and Electronics, where it is used to explain the Tunnel Diodes and the Tunnel Field Effect Transistors, in Biology, to explain the spontaneous DNA mutation, it is used in the Scanning Tunneling Microscopes, and many other examples[12].

Of course, we should be very happy that the temperature of the Sun is not higher because if the temperature was higher, the proton-proton reaction could happen more often and the hydrogen inside the Sun would be consumed faster.

The fact that the temperature inside the Earth is not so high imply that the electrons canít abandon their nuclei and the result is that when two atoms collide the electrostatic repulsion between electrons conspire to avoid the nuclei getting close. That is why we canít expect to have the creation of new elements inside the Earth, or inside any other planet as long as the temperature is not big enough for the electrons to be able to abandon the atom. That means all chemical elements we have in the Earth, came from outside!

††††††††† STARS EVOLUTION:

††††††††† As we discussed before, inside the Sun we find the process of transformation of hydrogen into helium. That is the way the Sun gets its energy. As a matter of fact, this is a very complicated process hindered by the fact that when two protons joint together, they canít create the nucleus He2 right away with just two protons. This system with only two protons is so unstable that most of the collisions result in re-emitting back the two original protons.

There is however other option: if the energy is big enough, one of the protons could transform into a neutron, emitting the excess of electric charge in form of a positron. Here we find a new, but very interesting problem. The positron that is totally similar to the electron but with positive electric charge, is a type of particle that is totally different from the proton. The proton (like the neutron) is member of the family called hadrons (their constituents are quarks), while the positron (like the electron) is member of the family called leptons.Based on the experimental results, it looks like the number of hadrons and leptons doesnít change in the Universe. That means that if you create a new hadron (or a new lepton) you have to create at the same time an anti-hadron (or an anti-lepton) so the number of these particles does not change.

As we said before, if the energy available is big enough, one of the protons can transform into a neutron, emitting the excess of electric charge in form of a positron. The neutron and the proton are the same type of particle, so no problem, but to create a positron (lepton) you have to create another particle or anti-lepton. Here is where the neutrino comes into live. The neutrino is an amazing new type of particle that is member of the lepton family but does not have electric charge and has (if any) a very small mass. The neutrino compensates the creation of the positron so that the total number of leptons does not change and makes possible the transformation of a proton into a neutron if there is enough energy available.

It is interesting that because the neutron mass is bigger than the mass of the proton, when we have a free neutron, it can transform spontaneously into a proton. Of course, to compensate for the proton positive electric charge an electron should be emitted, and to compensate the lepton electron charge, an anti-neutrino will be emitted. This process is called beta decay. The proton has a mass smaller than the mass of the neutron and that is why the proton canít transform spontaneously into a neutron, but if there is some additional energy available then the process could go through. That energy could be obtained from the kinetic energy associated with the motion of the protons.

Now we can explain how the Sun gets its energy burning hydrogen: two protons (hydrogen) transform into a deuterium (1 proton + 1 neutron) emitting a positron and a neutrino. The deuterium was discovered in 1932 by the American physicist Harold Urey.

†††††††††

[1] Science Desk Reference. ISBN 0-471-35675-1.Scientific American Page 241.

[2] http://en.wikipedia.org/wiki/History_of_the_Earth

[3]Science with the VLTI. European Suthern Observatory. 2008-08-08. Retrieved 2011-04-11.

[4] http://www.iupui.edu/~g115/mod04/lecture03.html

[5] http://www.schoolphysics.co.uk

[6] Steven Weinberg. The First Three Minutes. A Modern View of the Origin of the Universe.. Basic Books ISBN 13:978-0-465-02437-7. Page 113.

[7] Handbook of Chemistry and Physics. David R.Lide 72nd Edition (1991-1992) Page.5-81

[8] http://www.hyy.com.cn/WhatIsShallowGeothermalEnergy.html

[9] http://ircamera.as.arizona.edu/astr_250/Lectures/Lecture_12.htm

[10] http://www.windows2universe.org/earth/Interior_Structure/interior.html

[11] http://phys.org/news/2013-11-proton-radius-puzzle-quantum-gravity.html

[12] http://www.nature.com/nature/journal/v479/n7373/full/nature10679.html

Updated 11/04/2014