My Math Forum Where did copper come from? Fun thread!

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 April 18th, 2014, 05:09 PM #2 Math Team   Joined: Dec 2013 From: Colombia Posts: 6,539 Thanks: 2144 Math Focus: Mainly analysis and algebra I remember from some pop-science book that, by early theories of the universe, stars would create the other elements by means of nuclear fusion. But then it was discovered that the conditions within stars would blow apart any nuclei larger than Hydrogen. So then the question became 'where did the heavy elements come from?'. In particular, where did the Carbon that forms the basis of life as we know it come from? I forget the name of the guy (Hibbert? Hubble?) who came up with some theory that allowed large volumes of Helium to be created, and those were able to be catalysts for other elements. Or something like that anyway. Thanks from Benit13 Last edited by skipjack; May 9th, 2014 at 04:40 AM.
 April 18th, 2014, 05:13 PM #3 Global Moderator     Joined: Nov 2006 From: UTC -5 Posts: 16,046 Thanks: 932 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms Well, when a mommy copper and a daddy copper love each other very much... Thanks from Benit13
 April 18th, 2014, 10:06 PM #4 Math Team     Joined: Jul 2011 From: North America, 42nd parallel Posts: 3,175 Thanks: 177 AFAIK- nuclear fusion stops at iron (element 26), no heavier elements can be formed by that process so copper (element 29) and all heavier than iron elements must be formed in supernova or neutron star collisions or fissioning of other materials (but then it would be radioactive) Cyprus has large copper deposits and the name of the country is related to the modern word 'copper' , but I don't know linguistic details in this matter. -AFAIK Last edited by skipjack; May 9th, 2014 at 04:42 AM.
 April 22nd, 2014, 02:04 AM #5 Senior Member   Joined: Apr 2014 From: Glasgow Posts: 1,924 Thanks: 627 Math Focus: Physics, mathematical modelling, numerical and computational solutions Thanks for the replies guys. I was beginning to think this thread was a failed experiment . Just for the record I will try and link wikipedia articles or papers where I can. It seems like you all understand already that the Big Bang, although it created all matter in the Universe, is not responsible for the production of copper. This is because numerical models and observational evidence shows that the products immediately after the Big Bang were basically only hydrogen and helium with small amounts of deuterium and lithium (although lithium is still a problem). So yes, stars are necessary for heavier elements of the periodic table to exist on Earth today. Link: Big Bang nucleosynthesis - Wikipedia, the free encyclopedia v8archie: yes! Historically there were issues with the source of heat generation from stars and once nuclear reactions had been proposed, it was difficult to consolidate the theory at the time with the conditions in stars. There was a famous paper published in 1957 (link below) that proposed a full, consistent theory of the synthesis of the elements from nuclear fusion, together with tons of experimental evidence for it. It revolutionised stellar evolution studies. Link: Original article on NASA ADS Link: B2FH paper - Wikipedia, the free encyclopedia P.S. the answer to the original question isn't there, but it's awfully close. CRGreathouse: Alas, they can never get an opportunity to be together because of a large Coulomb barrier! Agentrredlum: Excellent! The binding energy per nucleon curve has a peak at iron, so it is possible for nuclear fusion in stars (provided the temperature and pressure is high enough) to form elements up to iron. This includes much of what is found on Earth, such as carbon, nitrogen, oxygen, silicon, aluminium, neon, etc. You are correct as well in saying that supernovae are required to form heavier elements, but the elements produced in the supernova explosion itself are mainly $\displaystyle \alpha$-elements. These are Ne-20, Mg-24, Si-28, and so on up to Nickel. Nickel then photodisintegrates (in the supernova and floating about in space) to form Fe-56, which subsequently becomes massively abundant in the universe and allows us to make steel for our cars and cutlery! The elements near iron are known as iron-peak elements. The $\displaystyle \alpha$-elements are formed by $\displaystyle \alpha$-particles capturing onto C-12 or O-16, or anything else in that chain. However, most of the elements after the iron-peak (such as copper, gallium, germanium, arsenic, ...) have a different mechanism responsible for their formation. Unfortunately, neutron star collisions and fission products are not the sources of copper, but you are thinking along the right lines. Neutron star collisions are very violent and are proposed as solutions for all sorts of problems in observations, but they cannot occur frequently enough to produce the relatively large amount of copper that is available in the solar system and throughout the Milky Way. Fission elements (such as uranium and plutonium) are rare in stars (although they ultimately exist on Earth and therefore there must be a source) and even if they were produced abundantly, they tend to create elements much heavier than copper. Massive stars and their supernovae are the right source, but charged-particle fusion cannot account for copper. For those who don't know about the binding energy per nucleon curve: Link: Nuclear binding energy - Wikipedia, the free encyclopedia For many details concerning massive stars evolution such as $\displaystyle \alpha$-element formation and supernovae: Link: Woosley and Weaver 1995 So... some questions to help spur things on are: i) if supernovae are required to create heavy elements, how did they end up on Earth? ii) how can copper be formed if it has such a large Coulomb barrier? (hint: it is nuclear fusion, but a particular kind... think of what kinds of particles exist and what things can fuse together to produce copper) Thanks from agentredlum Last edited by Benit13; April 22nd, 2014 at 02:07 AM. Reason: typos
 April 22nd, 2014, 02:58 AM #6 Math Team     Joined: Jul 2011 From: North America, 42nd parallel Posts: 3,175 Thanks: 177 Nice post Benit13, For question i), my thought's are: The first generation stars (now mostly long gone) that went explosive supernova seeded the the rest of the galaxy with heavier elements and these heavier elements coalesced in 'clumps' on the accretion disc of birthing star systems, and the seeding in fact may 'trigger' interstellar gas to come together and form a new star system. For question ii), I read most of the wiki link, > 1/2, and maybe I have an idea based on the quote below from the wiki link, "To reduce the disruptive energy, the weak interaction allows the number of neutrons to exceed that of protons—for instance, the main isotope of iron has 26 protons and 30 neutrons. Isotopes also exist where the number of neutrons differs from the most stable number for that number of nucleons. If the ratio of protons to neutrons is too far from stability, nucleons may spontaneously change from proton to neutron, or neutron to proton." So, in my 'pedestrian' understanding, it looks like copper can come from an iron isotope with 26 protons and 32 neutrons, 3 neutrons spontaneously change into protons, the change mediated (facilitated) by the weak interaction, and we get copper. Last edited by skipjack; May 9th, 2014 at 04:48 AM.
 April 22nd, 2014, 05:43 PM #7 Math Team   Joined: Dec 2013 From: Colombia Posts: 6,539 Thanks: 2144 Math Focus: Mainly analysis and algebra I think I might like some idea of the relative abundance of Copper in the universe and on earth before I try to come up with any theories. Universe: $6 x 10^{-6}%$ Earth's Crust: 0.0068% So, perhaps when we get large accretions of iron at high pressure and temperature, some of it can convert to copper following a process similar to that suggested by agentredlum. I'm particularly wondering if the core of a planet might suffice for this, although it does sound a bit unlikely. Last edited by v8archie; April 22nd, 2014 at 05:54 PM.
April 22nd, 2014, 08:39 PM   #8
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 Originally Posted by v8archie So, perhaps when we get large accretions of iron at high pressure and temperature, some of it can convert to copper following a process similar to that suggested by agentredlum. I'm particularly wondering if the core of a planet might suffice for this, although it does sound a bit unlikely.
That does sound unlikely to me, considering that the matter just came from a star which had much higher pressure and temperature.

 April 22nd, 2014, 09:41 PM #9 Math Team   Joined: Dec 2013 From: Colombia Posts: 6,539 Thanks: 2144 Math Focus: Mainly analysis and algebra And most of the reason for the increased percentage of copper on earth is probably the relative lack of hydrogen and helium. I have just read this though, which suggests that copper was created within giant stars during their lifetime, not as they went supernova. It's 2009 vintage though, so perhaps is out of date. Last edited by v8archie; April 22nd, 2014 at 09:47 PM.
 April 23rd, 2014, 05:30 AM #10 Senior Member   Joined: Apr 2014 From: Glasgow Posts: 1,924 Thanks: 627 Math Focus: Physics, mathematical modelling, numerical and computational solutions Interesting... Agentredlum: Not far off! Regarding your first comment, you are dead right when you say that supernova ejecta can become the matter from which other stars form. In fact, there is evidence that 100s of generations of massive stars have birthed, evolved and exploded to form a processing engine for the elements, giving us what we have today on Earth. Some researchers are looking at star formation histories in order to piece together the details about how each generation feeds to the next. Link: Recent review of star formation histories When scientists conduct computer simulations of stars the two main input parameters are the initial mass (say, for example, 15 Suns, aka solar masses or $\displaystyle M_{\circ}$) and the 'metallicity', which is a parameter that is basically the percentage of the star that is not made of hydrogen or helium. There is also a range of literature looking at particular abundance distributions for scientists to use as input in their work and matches with observations. It's an ongoing effort. Below is a very famous article compiling solar observations and meteorite data to compile a table of the solar abundances. Unfortunately it is not freely available to read. Link: Anders and Grevesse 1989 Note also that there is no need for a trigger or for the matter to appear/collide/interact on an existing accretion disc; the accretion disc is a natural consequence of matter coming together, so as long as there is supernova ejecta in some vicinity where mass is collecting together, an accretion disc can form and a star could be born if there is enough stuff. The dynamics of this sort of system are rather complex. Regarding your proposal to answer the second comment, you are referring to beta decays (both $\displaystyle \beta^+$ and $\displaystyle \beta^-$). This is an important ingredient for the mechanism that forms copper but there is something else too which is necessary because you cannot form the unstable isotopes that beta-decay without something else going on... v8archie: CRGreathouse is right, the temperatures and pressures are too low outside of stars for charged-particle fusion reactions to create all the heavy elements observed on Earth and even in massive stars you cannot form copper using this kind of reaction, because the Coulomb barrier is just too high. Besides, the binding energy per nucleon curve tells us that energy is no longer liberated by nuclear fusion reactions past iron, so massive stars will never obtain the temperatures and pressures necessary for it to occur. I like how you put numbers on the abundances though, as it gives a clear indication about how much copper needs to be made. These are exactly the kind of numbers that scientists worry about! Link: Wikipedia article with a graph showing observed abundances of elements in the Sun You are dangerously close to cheating by looking at that article, but I'm not fussed the article is slightly out of date in that a more recent article proposes something else, but the fact that copper can be produced during the lifetime of the star is definitely something to think about. More questions to think about: i) Agentredlum suggested that weak interactions (more specifically, $\displaystyle \beta$-decays) can form copper. Close... however, what forms the unstable isotope (which shall remain nameless!) in the first place? Hint 1: think of the fundamental particles of nature and interactions involving them. Hint 2: the reaction must get past or ignore the Coulomb barrier. ii) v8Archie found out that copper could be made during the lifetime of a massive star. How do massive stars evolve and how different are they to the Sun? This will really help get close to the answer

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