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The Origin of the Elements a) Formation of Light Elements

Image from http://helios.gsfc.nasa.gov/nucleo.html

b) Formation of Heavy Elements

http://www.shef.ac.uk/physics/teaching/phy320/topic6.html

The Origin of the Elements  Lab 10  1

Part 1 — Abundances Only hydrogen, some helium and small amounts of Beryllium, Lithium, and Boron are produced during the Big Bag. Other elements that are lighter than iron are made in stellar interiors, heavier ones are made during supernova explosions. So how are the elements made? You will find that out in Part 2. Let’s first determine how abundant the elements are. The figure below summarizes the results.

Image from http://www.daviddarling.info/images/cosmic_abundance.jpg The y-axis gives you the abundance of elements in the universe relative to hydrogen. For example, Iron, which has an atomic number of 28, has a corresponding abundance at roughly 10-5. This means it is 10-5 less abundant than hydrogen, or in other words, for every 100,000 H atoms you will find one Fe atom in the universe. Answer questions 3 to 5 after finishing the rest of the lab. 1. How big is the probability that an element is Helium? 2. How big is the probability that an element is Carbon? 3. Why do you think that the probability of obtaining heavier elements decreases with the atomic number of the element?

4. Why do you think that Beryllium, Lithium and Boron are rare compared to heavier elements?

5. Why do you think there is a secondary peak for Iron?

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Part 2 — Hydrogen Burning a) Making Helium from Hydrogen

4H Æ 1He + ν + e+ + Energy Helium Hydrogen

positron

neutrino

Figure from http://www.opencourse.info/astronomy/introduction/12.sun_interior/ This means that four protons (or Hydrogen nuclei) fuse to form one Helium nucleus. In that process positrons (electrons with positive charge) and neutrinos are emitted and a lot of energy is produced. This is the overall process. Details are described in sections b, c, and d. We will be using a certain way of writing nuclear reactions by using a shorthand. Helium has an atomic number of 2, so it has 2 protons. The stable isotope of Helium is Helium-4, i.e., the isotope of Helium that has 2 neutrons and 4 nucleons (2 protons + 2 neutrons). This is written as follows: number of protons + neutrons 4 2

He

number of protons

b) Hydrogen burning in low mass stars and details of the p-p chain The above picture and equation is a little oversimplified. The process of fusing hydrogen to helium proceeds in three separate steps. In each step protons are added. That’s why this process is called the p-p chain. It happens in low mass stars. Here is a picture of what is happening: Two protons fuse to form Deuterium. Then another proton fuses with deuterium forming helium-3 (an unstable isotope of helium). Two of those helium-3 nuclei then fuse to form the stable isotope of helium (helium-4). In that process two protons are emitted. 1 1

H +11H →12H + 10e+ 00ν

2 1

H +11H →23He+ 00γ

3 2

He+ 23He→24He+11H +11H

(where ē is a positron — an electron with a positive charge, ν a neutrino, and γ a gamma ray)

The Origin of the Elements  Lab 10  3

If you don’t like symbols and equation, the picture below shows this graphically:

From http://outreach.atnf.csiro.au/education/senior/cosmicengine/stars_types.html This may look to you like a chemical reaction, but it is not. We are dealing with nuclear reactions and we are making elements, not molecules. Like in chemistry, there are certain rules for these reactions. a) The total number of nucleons (n + p) is conserved (is the same on both sides). b) Charge is conserved (is the same on both sides). Sometimes a proton may fuse with helium-3. Based on the above reactions, complete the following: 3 2

He + 11H →

4 2

He +

+

What are the names of the elementary particles that are produced along with helium-4?

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c) Hydrogen burning in high mass stars and details of the CNO cycle More massive stars have more gravitational energy, so the core of the star may get relatively hotter than in low mass stars. When the temperature is hotter, the elements move faster, and heavier elements (that also have a higher charge) move fast enough so that they may crash into each other. Thus heavier elements may take part in the nuclear burning process, however, they only act as catalysts. The individual steps are shown below. In these reactions hydrogen is fused to helium, and the other elements (Carbon, Oxygen and Nitrogen) take part in the reaction by are restored. This process of burning hydrogen is called the “CNO” cycle since it involves Carbon, Oxygen and Nitrogen

From Wikipedia at http://en.wikipedia.org/wiki/CNO_ l Take a colored pencil and mark all hydrogen atoms in one color, all Helium atoms in another. Ignoring what happens to Carbon, Nitrogen and Oxygen, write down the OVERALL reaction of the CNO cycle.

How is this reaction different from the p-p chain? The final outcome is the same, so why do you suspect low mass stars do not burn hydrogen via the CNO-cycle? And what do you suspect is the effect of burning H via the CNO cycle in massive stars?

The Origin of the Elements  Lab 10  5

d) Determining the Energy that is produced (Uncertain about how to do this? Check you lecture notes and/or your book.) In the process of turning hydrogen to helium, mass is lost. This mass gets transformed to energy (remember Einstein’s E=mc2?). Calculate how much energy is released when burning 1 kg H to He. [Hint: First, calculate the difference in mass when burning 4 H nuclei into one He nucleus (the masses are in the toolkit), then figure out the percentage of mass that is lost and determine how much mass is lost when using 1 kg of hydrogen. Finally plug that into the famous formula to calculate the energy. State your answer in Joules.]

Now this number is meaningless unless we compare it to another energy source that you can relate to. So next figure out how many kilograms of coal you would have to burn in order to get the same energy output as from burning 1 kg of hydrogen. Burning 1 kg of coal produces about 5x106 Joules of energy. How much more energy is produced by burning hydrogen to helium?

This number is another incredibly large meaningless number. Let’s figure out for how long you can supply energy to power the entire city of New York. Find this number on the web, and determine how long this energy would last.

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Part 3 – Helium Burning The Triple Alpha process proceeds in two steps. First, two helium nuclei combine to form beryllium, and then the beryllium nucleus combines with another helium nucleus to form carbon. The detailed steps are:

This reaction has to occur in two different steps, otherwise you would have to collide 3 helium nuclei in one single instant. So therefore, first beryllium is formed, then carbon. Nevertheless, let’s simplify the overall process in a schematic drawing:

From http://www.astro.cornell.edu/academics/courses/astro201/helium_burn.htm In the above drawing, carbon is represented by one nucleus. Using colored pencils, draw the carbon atom illustrating the number of protons and neutrons.

The Origin of the Elements  Lab 10  7

Part 4 –Carbon Burning Like in the previous case, heavy elements can be formed by fusing the nuclei; for example:

http://www.astro.cornell.edu/academics/courses/astro201/carbon_fusion.htm The formation of even heavier elements (up to Iron) is summarized by:

From http://astronomy.nmsu.edu/tharriso/ast110/class19.html Write down a reaction of how to make Silicon. Write down a reaction of how to make Sulfur. Write down a reaction of how to make Iron.

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Part 5 — Burning Elements heavier than Iron

Fusion

Fission

From http://www.alaskajohn.com/physics/ This is a plot of the binding energy per baryon as a function of the atomic weight of each element. The binding energy is defined as the energy required to keep the nucleons together. Look at the above plot. In which element are the nucleons held together most tightly – i.e., which is the heaviest element that has the highest binding energy per baryon?

In heavier elements the baryons are not as tightly bound together, which means that those elements can break down into lighter ones, i.e., fission may happen. This explains the arrow in the above plot. In contract, lighter elements can fuse together. Explain why you can only make the elements up to iron in stellar interiors.

How and where could elements heavier than Iron be formed?

The Origin of the Elements  Lab 10  9

Element Formation and Supernovae Elements heavier than Iron get created during Supernova Explosions. Since there are two types of supernovae (SN I and SN II — the end stage of a low mass binary and the end stage of a high mass single star), the details are a little different, but the general process is the same. Prior to the explosion, the electrons in the progenitor (the Iron core in the case of the massive star and the Oxygen/Carbon core in the case of the White Dwarf) become degenerate. Any increase in temperature is no longer counterbalanced by an increase in pressure. This gives rise to a “run-away-process” which results in the photo-dissociation of the Iron or the Oxygen and Carbon nuclei into α-particles (alpha particles — these are Helium nuclei). These disintegrate into protons and neutrons. Following that, the protons combine with electrons to form neutrons and anti-neutrinos. This process requires energy. It can be expressed by:

p + + e- → n + ν e The core collapses into a neutron star in the case of the low mass binary and in the case of a massive star. In the case of a very massive star, where the core is larger than about 8 Mℵ, the core collapses into a black hole. During the explosion, so much energy is emitted that heavy elements can be created. In principle, the large fractions of neutrons that have been created crash into the nucleus of other elements. This results in making different isotopes of the same element. Often, these isotopes are unstable, and will decay (actually β-decay, i.e., lose an electron) emitting lots of energy. This process is known as radioactive decay. Here is an example of such nucleosynthesis, starting with the stable isotope of Iron. 56 26

Fe+ 01n →57 26 Fe

57 26

58 Fe+ 01n →26 Fe

58 26

Fe+ 01n →59 26 Fe

59 26

Fe+ 01n →60 26 Fe

60 26

61 Fe+ 01n →26 Fe

61 Now, 26 Fe is stable for only 6 minutes, and if no further neutrons are captures in that time, it will βdecay such that one of the neutrons in the nucleus turns into a proton while emitting an electron and a neutrino.

It is the same reaction as before, with the difference that energy is released. n → p+ + e− + ν e So then, the 61 26

61 26

Fe -isotope of Iron decays into Cobalt. The reaction for this is:

61 Fe→27 Co + e − + ν e

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In the same fashion, other elements can get created. The schematic diagram below shows a series of such processes. The x-axis shows the number of neutrons, and the y-axis shows the number of protons. In this diagram, let’s follow how starting off with Cadmium (Cd) and bombarding that with neutrons, produces Indium (In), then Tin (Sn), and finally Antimony (Sb). First find Cadmium-110. Cadmium110 has 48 protons (check the periodic table) and 110-48=62 neutrons. So, Cd-110 is the box where the x-axis is 62 and the y-axis is 48. Follow the arrow. Cd gets bombarded with one neutron forming Cd111, which occupies the box where the x-axis now is 63 and the y-axis is still 48. This process continues until Cd-115 is formed. This then β-decays to Indium-115 ( 115 49 In ).

Write out the series of reactions to create Indium from Cadmium.

110 48

Cd + 01n →

111 48

Cd + 01n → +

→

+

→

+

→

→

111 48

Cd

+ e− + ν e

The Origin of the Elements  Lab 10  11

Lab Report 1) Objective of the Lab

2) Now you have all elements – and it’s a long, long step to make humans from these elements. Suggest how this could happen.

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