Genesis of the Elements

Overview

In this article we'll be discussing many topics that are central to modern astronomy and cosmology including Rutherford's gold foil experiment, the Big Bang, Big Bang and stellar nucleosynthesis, the event of recombination, and how most of the elements in the period table come from the life-cycles and deaths of stars. George Gamow realized that Lametre’s Big Bang theory implied that the universe was once very small, dense and hot. He theorized that during the time between when the universe was only one second old to when it was about three minutes old, conditions were right for hydrogen and helium to form. But where did the heavier elements in the periodic table come from? Fred Hoyle used nuclear physics to determine the life cycles of small, medium, and big stars. He discovered that light to medium-sized elements were created via nuclear fusion occurring within the interior of stars and that the heavier elements were created by the nuclear reactions which occurred in supernovae explosions—an event which occurs at the end of a very massive star's life. Big Bang and stellar nucleosynthesis, together, account for where almost all of the elements in the periodic table come from.

Rutherford's experiment

                                        This video was produced by the Khan Academy.

Maria and Pierre Curie demonstrated through a series of experiments that very heavy atoms, such as uranium and radium, spontaneously emitted radiation and in the process released stupendous amounts of energy. This phenomenon, known as radioactivity, overturned the prevailing view in the nineteenth-century that the atom was some kind of plain, structureless sphere. In 1904 the physicist J. J. Thompson proposed a new model of the atom known as the plum pudding model which pictured the atom as a kind of positively charged dough (the pudding) with negatively charged particles (the plums) embedded within it. This model attempted to explain one form of radioactivity involving the emission of alpha particles (an alpha particle is two protons and two neutrons bounded together) as ejected pieces of positively charged dough.

In 1909 Ernest Rutherford and his two colleagues, Hans Geiger and Ernest Marsden, conducted an experiment in which they probed the structure of the atom by directing a beam of alpha particles towards a gold foil. Most alpha particles were transmitted through the foil, with only slight deviations in their motion, and struck a zinc sulphide screen on an alpha detector releasing a flash of light which Geiger and Marsden observed through a microscope. Rutherford decided “for the sheer hell of it” to instruct Geiger and Marsden to move the alpha detector to the same side of the apparatus that the radium was on and to his astonishment discovered that 1 in every 8,000 alpha particles arrived at the detector. This result contradicted Thompson’s plum pudding model and compelled Rutherford to formulate a new atomic model which would make predictions that agreed with his experiment. He pictured the atom as being composed of tiny, positively charged spheres (called protons) located at the center of the atoms (called the nucleus) with tinier, negatively charged spheres (called electrons) orbiting the nucleus. (This is analogous to our model of the solar system in which the planets orbit around the Sun.) He calculated that the diameter of the atom must be smaller than one-billionth the size of a meter and the diameter of the nucleus must be about 100,000 times smaller than that of the atom. This model explains the results of the experiment: most alpha particles pass right through the gold foil since it is mostly empty space, but occasionally an alpha particle will collide with a nucleus of a gold atom causing it to be rebounded at some angle. Rutherford also predicted that there should be another kind of particle (called a neutron) located at the atom’s nucleus. The existence of the neutron would later be experimentally demonstrated by James Chadwick in 1934.

 Figure 1: Rutherford's experiment involved putting a radioactive element known as radium inside of a lead box. The radium spontaneously emitted \(α\) particles in a narrow beam through a small hole in the box. These \(α\) particles were directed towards a gold foil. Most \(α\) particles passed straight through the gold foil but occasional one would get reflected back at an acute angle with the beam of \(α\) particles. This meant that atoms must have tiny, but very dense, nuclei.  Image credit: http://m.teachastronomy.com/astropedia/article/The-Structure-of-the-Atom

Figure 1: Rutherford's experiment involved putting a radioactive element known as radium inside of a lead box. The radium spontaneously emitted \(α\) particles in a narrow beam through a small hole in the box. These \(α\) particles were directed towards a gold foil. Most \(α\) particles passed straight through the gold foil but occasional one would get reflected back at an acute angle with the beam of \(α\) particles. This meant that atoms must have tiny, but very dense, nuclei. Image credit: http://m.teachastronomy.com/astropedia/article/The-Structure-of-the-Atom


What makes stars shine? Where do lighter elements come from?

 Figure 2: All stars in the universe generate light and energy by fusing lighter elements into heavier elements. For stars up to the mass of about that of our Sun, light and energy is created by fusing hydrogen into helium. The image above illustrates the chain of nuclear reactions which occur in small to medium sized stars and very massive stars that allow them to generate light and energy. Stellar fusion accounts for where many of the light to medium-sized elements in the periodic table come from.

Figure 2: All stars in the universe generate light and energy by fusing lighter elements into heavier elements. For stars up to the mass of about that of our Sun, light and energy is created by fusing hydrogen into helium. The image above illustrates the chain of nuclear reactions which occur in small to medium sized stars and very massive stars that allow them to generate light and energy. Stellar fusion accounts for where many of the light to medium-sized elements in the periodic table come from.

Rutherford’s newfangled atomic model accurately described radioactivity as transformations which took place in the nucleus of an atom: protons within the nucleus could transform into neutrons and vice versa, or alpha particles could be ejected from the nucleus. It also described nuclear fission—which is when nucleons (protons and/or neutrons) are ejected from an atom’s nucleus—and nuclear fusion which is when two or more atomic nuclei fuse together. The incredible amount of energy released in these processes is generated from mass transforming into energy according to the famous equation, \(E=mc^2\). When a radium nucleus fissions into an alpha particle (two protons plus two neutrons) and a radon nucleus, the combined mass of the alpha particle and radon nucleus is less than the mass of the radium nucleus. This “missing mass” was transformed into energy. When nuclear fusion occurs and two or more atomic nuclei fuse together the total mass of the system decreases by \(Δm\) and is transformed into energy (according to \(E=Δmc^2\)). Since all atomic nuclei are positively charged and like charges repel one another via the electric force, the only way atomic nuclei could fuse together is if they got very close. The strong nuclear force is a “short-ranged force” which can pull nucleons together; but only if their separation distance is very small. This force is about 100 times stronger than the electric force, strong enough for atomic nuclei to overcome the repulsive electric force and fuse together. In 1929 the physicist Fritz Houtermans along with a scientist named Robert d’Escourt Atkinson published a paper in the journal Zeitschrift fur Physik in which they used nuclear physics and Einstein’s energy-mass equivalence principle (\(E=mc^2\)) to provide the first explanation to the question: what makes the stars shine? Houtermans calculated that if the separation distance between two atomic nuclei is \(10^{-15}\) meters, the strong force will be “in range” and fuse them together converting mass into light energy.

Houtermans and Atkinson believed that the temperatures and pressures within the Sun’s core were high enough for hydrogen nuclei to come within \(10^{-15}\) meters of each other and fuse into helium releasing energy in the form of light. Due to a series of emigrations and persecutions Houtermans was unable to complete his work. Hans Bethe picked up where Houtermans left off and (by applying the rules of nuclear physics to the atoms in the Sun’s core) identified all the nuclear reactions occurring within the Sun’s interior which are responsible for manufacturing helium nuclei from hydrogen nuclei.


Hydrogen and helium were created during the Big Bang

Figure 3: The Alpha-Beta-Gamma paper demonstrated that after the first roughly three minutes of the universe since its initial Bang, hydrogen and helium nuclei were synthesized via nuclear fusion. After about three minutes, the universe cooled enough for fusion to stop; but the universe was still so hot that all of the matter comprising the universe was a plasma and plasma's are opaque to radiation. The matter comprising the universe was in a plasma state for the first roughly 300,000 years since the Big Bang; since plasma is opaque to radiation, for the first roughly 300,000 years light could not freely travel throughout the universe without constantly "bumping into stuff (atomic nuclei)." At sometime when the universe was about 300,000 to 400,000 years old, matter cooled enough for electrons to bind to atomic nuclei and for light to freely pass through the universe. Due to the expansion of space, Alpher and Herman estimated that wavelengths of this light should now be stretched into the microwave region.

George Gamow noticed that these men’s work ostensibly failed to account for the creation of the heavier elements. Gamow wanted to see if Lametre’s Big Bang theory predicted the conditions necessary for nuclear reactions to occur that would create all the elements in the periodic table.

The two most important parameters to consider (which determine what kind of nuclear reactions take place) are temperature and pressure. Gamow took the Big Bang theory and “ran the clocks backwards” to see what would happen to the temperature and pressure of the universe. He realized that the temperature and pressure would keep increasing until they become so high that protons, neutrons and electrons could not bind together—conditions too extreme for nuclear fusion to occur. According to the Big Bang theory, if we run the clocks backward in time far enough (but not too far) there will be a particular “window of time” (when the universe was about \(1\) second old to when it was about \(3\) minutes old) when the universe was billions of degrees (but not millions or trillions of degrees) and hot enough for hydrogen and helium (and their isotopes) to form. If we go back too far in time the universe was trillions of degrees and too hot for even atomic nuclei to form. If we don’t go back in time far enough the universe was too cold and particles didn’t have enough energy for nuclear fusion to spontaneously occur. The Alpha-Beta-Gamma paper demonstrated that during this special window of time (during, roughly, the first three minutes of the universe's life) the conditions were right for hydrogen and helium nuclei to form in the right proportions (meaning the proportions that we measure today).

This is the second major piece of evidence supporting the Big Bang theory. But the major limitation of this paper was its inability to explain how the heavier elements (heavier than helium) formed during this special time period of nucleosynthesis. Independent research by nuclear physicists Enrico Fermi and Anthony Turkevich agreed with the paper and predicted the correct amounts and proportions of all isotopes of hydrogen and helium.

Shortly after this time period the universe cooled and became millions of degrees—too cool for nuclear fusion to continue to occur. The matter in the Universe was something called a plasma. A plasma is a state of matter where the temperature is so high that electrons cannot be bounded to atomic nuclei—essentially it is a “soup” of atomic nuclei and electrons whizzing by one another. Thus all the matter in the universe behaves like an electrical conductor and electrical conductors are opaque to radiation. Alpher and Herman estimated that sometime around 300,000 years after the birth of the Universe (see Figure 3), the universe (due to the expansion of space as discussed earlier) became too cool for the matter to be a plasma. The temperature at which matter becomes to cool to be plasma is \(~3,000K\) or about half as hot as the surface of the Sun. Around this time the universe cooled enough for atomic nuclei to become bound to electrons—an event which is called recombination. (This name is somewhat confusing since nothing is actually being “recombined.”) All the matter in the Universe underwent a phase change from being plasma to being a gas. For the first time the Cosmos lit up and became transparent to light.


The sky should be filled with microwaves, everywhere!

"When was the first time that the Universe cooled down enough that light could finally move around?" This video was produced by Fraser Cain.

Based on the relationship between temperature and wavelength (something that we discussed in detail in other lessons), Alpher and Herman calculated that at the time of recombination the wavelengths of light must have been roughly one-thousandth of a millimeter.

According to the Big Bang Theory and nuclear physics, this radiation should be coming from all directions in the night sky since when it was initially emitted during recombination it was present everywhere throughout the Universe. From the expansion of space Alpher and Herman calculated that, by today, the wavelength of this radiation should have been stretched by a factor of 1,000 and be one millimeter.

This wavelength corresponds to the microwave region. Later on this microwave radiation was detected at the Bell Laboratory in New Jersey which was the second great triumph of the Big Bang theory.


Heaviest elements are created through the life cycles and deaths of stars

Figure 4: As a star undergoes nuclear fusion in its core, it generates light. This light exerts an outward radiation pressure on the star which balances the inward gravitational forces that tend to pull the star's matter towards its center. But at the end of a star's life, nuclear fusion begins to slow down and eventually stop; this means that there is no outward radiation pressure to balance the gravitational forces exerted on the outward layers of the star and star eventually collapses. If the star is very massive, such a collapse will result in one of the most spectacular events in the universe: a supernova. The energy generated by a supernova explosion is so stupendous that it results in nuclear reactions which create the heavier elements in the period table.

Shortly after later astronomers corrected Hubble’s distance measurements, Edington speculated that perhaps elements heavier than helium are created by stars. A cosmologist named Fred Hoyle made the most significant contributions to the longstanding problem on how the heavier elements were created.

He thought about the various phases a star underwent throughout its life. For the majority of a star’s life the radiation created in its center (due to nuclear fusion) exerts an outward pressure on all the masses in the outer layers of the star which effectively counteracts and balances the inward gravitational pull of all the masses. This is what prevents the star from collapsing. But towards the end of a star’s life its hydrogen fuel eventually starts to run out and the temperature in the star’s interior decreases. Thus a smaller number of photons which are less energetic are getting emitted in the center of the star and the inward gravitational forces eventually overpower the outward radiation pressure causing the star to contract. The star will then proceed to go through a series of stop-start spasms. As the star starts to contract due to the dwindling amount of hydrogen fuel, it temporarily starts to heat up and increase the pressure of the stellar core causing the contraction to temporarily halt. But then eventually the star begins to contract again.

These phases of contractions and momentary pauses continues for a little while until the star eventually collapses into either a neutron star, a white dwarf, or a black hole. Hoyle calculated—for many different kinds of stars including small-sized stars, medium-sized stars, etc.—that the nuclear reactions which occurred during these final phases of the star’s life would lead to the creation of many of the heavier elements. He theorized that some stars would be so massive that they would very rapidly collapse resulting in a supernova. He calculated that the heaviest and rarest elements in the periodic table could be created in the nuclear reactions which occurred in a supernova. Since we humans and indeed all life on this planet are made of mostly heavier elements, we could not be here if stars did not die. In the words of Carl Sagan,"We are made of star stuff. We are a way for the cosmos to know itself." Hoyle’s theoretical work on where the heavy elements come from is widely recognized as one of the greatest triumphs of the 20th century in science.

In summary, Gamow showed that the lighter elements (hydrogen and a little bit of helium) were created by the nuclear reactions which took place during a small time interval within the first three minutes of the Big Bang whereas Hoyle showed that the “medium sized” elements were created by the nuclear reactions occurring within the center of stars and the heavy elements were created by the nuclear reactions occurring within a supernova explosion. Together their work explains where most of the elements in the periodic table come from.


This article is licensed under a CC BY-NC-SA 4.0 license.

References

1. Singh, Simon. Big Bang: The Origin of the Universe. New York: Harper Perennial, 2004. Print.

2. Wikipedia contributors. "Big Bang nucleosynthesis." Wikipedia, The Free Encyclopedia. Wikipedia, The Free Encyclopedia, 12 May. 2017. Web. 18 May. 2017.

3. Khan Academy. "Rutherford's gold foil experiment | Electronic structure of atomis | Chemistry | Khan Academy". Online video clip. YouTube. YouTube, 23 November 2015. Web. 06 November 2017.

4. Fraser Cain. "When was the First Light in the Universe? Seeing As Far Back As Possible". Online video clip. YouTube. YouTube, 04 November, 2016. Web. 06 November 2017.