Energy Generation in the Sun and Origin of Heavy Elements ASTR 1115G October 2024 PDF

Energy Generation in the Sun and Origin of the Heavy Elements ASTR 1115G October 8, 2024 Kamioka Observatory, ICRR (Institute for Cosmic Ray Research), The University of Tokyo Announcements Please put away phones and headphones/earbuds. Put smart watches on DnD...

Energy Generation in the Sun and Origin of the Heavy Elements ASTR 1115G October 8, 2024 Kamioka Observatory, ICRR (Institute for Cosmic Ray Research), The University of Tokyo Announcements Please put away phones and headphones/earbuds. Put smart watches on DnD Grades now visible on Canvas Includes Midterm 1 Labs meet at football stadium this week  Conflicting evidence Geologists independently found that Earth must be >4 http://mspostons3rdgrade.weebly.com/fossils.html billion years old. Solution: This is was an enormous Nuclear Energy discrepancy! Gravity: 1 x 106 years Fossils: 4 x 109 years  Atomic Nucleus In 1911, it was discovered that all of a gold atom’s positive charge is concentrated into a tiny nucleus. This was a big surprise! It implies the existence of a strong nuclear force. The idea is that, although protons do repel each other through the electrostatic force, if they get very close, then they attract each other through the much stronger strong force, which can make protons stick together as long as they’re already very close. It’s sort of like glue.  Isotope Notation Used to indicate mass (top number: nucleons = protons + neutrons) and atomic number (bottom number: the number of protons) in a nucleus. 1 1 H This hieroglyphic describes a nucleus that has 1 nucleon, and one proton. So evidently there are no neutrons. This is ordinary hydrogen. H 2 1 This describes a nucleus that has 2 nucleons, and one is a proton. So evidently there is one neutron. This is “deuterium” or “heavy hydrogen”. It occurs naturally, but is poisonous in large quantities.  Isotope Notation 14C 6 This describes a nucleus that has 14 nucleons, and 6 of them are protons. This is “carbon 14”, which is radioactive. 12C 6 This describes a nucleus that has 12 nucleons, and 6 are protons. So evidently there are 6 neutrons. This is ordinary carbon. Here is carbon 13, which is also stable: 13C 6 Isotope Notation: Your turn! How many protons and neutrons? How many protons and neutrons? 15O 235U 8 92  Nuclear Decay Atoms that are unstable (unfavored ratio of neutrons to protons) decay into nuclei that are more stable. Example: Decay of carbon-14 (radioactive) into nitrogen-14 (stable) via electron emission: 14 C6 → 14N7 + e- +νe This means: an (unstable) 14C6 nucleus spits out an electron and something called an electron antineutrino. Afterwards, it has turned into a 14N7 nucleus. This result is a specific case of the preferred nuclear ratio of 1 neutron per proton, which holds up to calcium. You don’t have to remember that.  Stability by Isotope For any given atomic species, some isotopes are stable and some are less stable, depending on the number of neutrons. There is a sweet-spot, and for lower or higher neutron numbers, lifetime shrinks. isotope half-life 10C 6 19.29 sec 11C 6 20.33 min 12C 6 stable 13C stable source: wikipedia 6 14C 6 5730 years 15C 6 2.45 sec 16C 6 0.75 sec  Concept: Binding Energy Energy is the ability to do work. It can be: kinetic (energy of motion) potential (stored energy in many forms) light (radiation) The Law of Conservation of Energy requires that energy is never created or destroyed, but it can convert from one form to another or be transported. Example 1: When you drive to a restaurant you start with potential energy stored in the chemical bonds in your gasoline. This is converted into kinetic energy as it’s burned to move your car. Then, when you use your brakes to stop, it’s converted into heat, which is just random kinetic energy of the atoms in your brakes. When your brakes cool, they radiate the energy away via infrared light.  Concept: Binding Energy Energy is the ability to do work. It can be: kinetic (energy of motion) potential (stored energy in many forms) light (radiation) The Law of Conservation of Energy requires that energy is never created or destroyed, but it can convert from one form to another or be transported. Example 2: When NASA sends a rocket to Jupiter, the rocket engine converts potential energy stored in the chemical bonds in the fuel into kinetic energy, which is used to move the rocket up; some of this is then converted into the rocket’s gravitational potential energy. If the rocket falls back down to Earth, then that potential energy converts back into kinetic energy. If it never returns, then the energy remains in that form.  Response Card Question Suppose that the sun contracts under its own gravity. If it does, then the Sun: A. Converts gravitational potential energy to thermal energy and heats up B. Converts chemical potential energy to light and cools C. Converts light into gravitational potential energy and grows dim D. Converts light into gravitational potential energy and grows brighter  Response Card Question Suppose that the sun contracts under its own gravity. If it does, then the Sun: A. Converts gravitational potential energy to thermal energy and heats up B. Converts chemical potential energy to light and cools C. Converts light into gravitational potential energy and grows dim D. Converts light into gravitational potential energy and grows brighter  Concept: Binding Energy Energy is the ability to do work. Can be: kinetic (energy of motion) potential (stored energy) light (radiation) Example 3: The strong nuclear force pulls nucleons together. Pulling the nucleons apart again takes energy (just like ripping apart two pieces of paper that are stuck with glue). The amount of energy necessary to dissociate a nucleus is its nuclear binding energy. The higher the nuclear binding energy, the more stable it is. You might say that protons and neutrons “like” to be in nuclei that have higher binding energy. Nuclear Binding Energy by Species Remember: higher Fission binding energy means a more stable Fusion nucleus. Nature “wants” nucleons to move into nuclei with high binding energy. source: Prof. Charles E. Sundin’s website Nuclear Binding Energy by Species From this chart, you can see that energy is released if a star takes Fission four protons (1H1) and fuses them into an Fusion ordinary helium (4He2) nucleus, because helium is above hydrogen on the vertical axis. source: Prof. Charles E. Sundin’s website Nuclear Binding Energy by Species The highest species on this chart is 56Fe. Fission This means that every nucleon “wants” to Fusion be in an iron nucleus. Any reaction that makes a nucleus more like iron releases energy. source: Prof. Charles E. Sundin’s website Nuclear Binding Energy by Species Fusion: Low-mass nuclei like 12C6 and 16O (carbon and 8 Fission oxygen) get closer to iron by fusing with Fusion more nucleons. So these reactions release energy. This happens mostly in stars. source: Prof. Charles E. Sundin’s website Nuclear Binding Energy by Species Fission: Massive nuclei like 235U92 (the Fission unstable version of uranium) get closer to Fusion iron by splitting into smaller nuclei. This is what happens in nuclear reactors. source: Prof. Charles E. Sundin’s website  2-Minute Recall Without referring to the previous slides, write down in two full sentences the differences between nuclear fission and nuclear fusion.  Fusion of hydrogen 4 1H1 → 4He2 + 2 e+ + 2 ν0 + γ Start with 4 protons. End with a helium nucleus and lots of extra stuff! Helium has a higher nuclear binding energy than hydrogen Energy is released This is what powers the Sun. credit: N. Vogt  Fusion of hydrogen Mass of 4 protons: 6.6943 x 10 -24 g Mass of one 4He2: 6.645 x 10-24 g The resulting helium nucleus is less massive than the original 4 protons. What happened? The difference is released in different ways, the majority of which eventually is released as the light that we see, feel, and use to grow our food. The amount of energy released can be estimated from Einstein’s famous relation between energy and mass, E = mc 2.  Nuclear Fission Atoms that are more massive than 56Fe30 tend to decay into products that are closer to the most stable of all isotopes, 56Fe30. Example: fission of 235U: credit: Jim Doyle, emc2-explained.info  Response Card Question Late in their lives, some stars extract energy from carbon. They do this via: Fission A. nuclear decay Fusion B. fission C. chemical reaction with O and H D. fusion source: Prof. Charles E. Sundin’s website  Response Card Question Late in their lives, some stars extract energy from carbon. They do this via: Fission A. nuclear decay Fusion B. fission C. chemical reaction with O and H D. fusion source: Prof. Charles E. Sundin’s website  Vocabulary This lecture had a lot of words that you may not know, or at most may only have heard. Take your pen and notebook and write down a definition for each of these words, referring back to these slides and your textbook as necessary. It will take time, but do this now! nucleus nuclear decay proton fission neutron fusion electron isotope stability and the nuclear binding energy  Main Points Atomic nuclei consist of very dense condensations of protons and neutrons. Protons and neutrons have nearly the same mass, but protons have a positive charge while neutrons have none. They both attract other nucleons via the strong force. For any atomic species, there is a most stable isotope corresponding to a preferred number of neutrons. There are three kinds of nuclear reactions that we touch on in this class: 1. Atoms that are unstable have an unfavorable ratio of protons to neutrons; they will decay or split into atoms that are stable. 2.Fusing smaller nuclei into large ones is generally exothermic (energy- producing) until the product is more massive than 56Fe30, and endothermic (energy-consuming) at higher masses. 3. Conversely, fission (splitting) of isotopes more massive than 56Fe30 is generally exothermic.