Energy of a nucleus

1. Energy of a nucleus Ch. 14 Themassofa heliumnucleus is slightlysmaller(<1%) thanthe combined masses of its four nucleons.This mass difference is converted to energy via E=mc2. Helium nucleus 2 protons 2 neutrons 6.645·10-27 kg 6.695·10-27 kg

2. Conversion of mass to energy 5·10-29 kg of mass is converted to energy when 2 protons and 2 neutrons are combined to form the helium nucleus: E=mc2=(5·10-29kg)·(3·108m/s)2 = 4.5·10-12J = 28MeV Each of the four nucleons releases 28 MeV / 4 = 7 MeV 1J = 6.24 1018 eV

3. · 1H Principleofnuclearfusion Energy is released when combiningtwolightnuclei into one heavier nucleus. Energy per nucleon in MeV 4He Ni Nucleon Number A Energy per nucleon Fe and Ni have are the most stable nuclei (lowest energy per nucleon).

4. Pu Plutonium Pu Fe Ni Nucleon Number A Fusion vs. fission • Energyisreleased either by combining two small nuclei(fusion)orbysplit-ting a large nucleus into two pieces(fission). • Theenergyisreleased as radiation and as kinetic energy. Both eventually turn into heat (the fire- ball fromanuclearbomb andthesteamgenerated in a nuclear reactor).

5. Fusion vs. fission in bombs, reactors • Fusionpowers hydrogen bombs. Fissionpowers atomic bombs. • Fusionhas not yet been tamed for peaceful purposes. Fission generates energy in nuclearreactors.

6. Fusion in stars • Stars convert hydrogento helium and heavier elements. When Fe and Ni are reached, fusion stops. The star has burnt its nuclear fuel and collapses under its own gravity. • In massive stars, this collapse releases a huge amount of gravitational energy that leads to a supernova.The outer 90% of the star is ejected,and thecenterbecomes either a blackhole(>3 solar masses) ora neutron star(between1.4 and 3 solar masses), where the atoms collapse into a single huge nucleus. Lighter stars become white dwarfs. • All elements heavier than iron/nickel are created during a supernova explosion,which has enough thermal energy to form nuclei with higher energy per nucleon.

7. Stable nuclei Red dots=stable nuclei. The gray region contains unstable nuclei, created in the laboratory. Stable nuclei have about equalneutronandproton numbersNandZ(dashed). At high Z, there are more neutronsthanprotons,be- causeprotonsarecharged and repel each other.

8. Radioactive decay If the ratio of protons to neutrons gets too far off-balance,a nucleus willspontaneously transform itself into another nucleus with a better ratio byemitting,,particles.  particle = 2p2n = He nucleus  particle = electron particle = photon Marie Curie, Nobel prizes in physics, chemistry

9. Different isotopes of the same element Isotopes Isotopes are differentversions of the same element (sameZ). Theyhavethe same numberof electrons and protons, but a different neutron number N. Theirchemicalbehavior is the same,sincethatisdetermined by the electron number (=Z). Stable isotopes are shown as red dots.The gray region con-tains unstable isotopes which are radioactive.

10. Tritium Deuterium Hydrogen One proton One protonone neutron One protontwo neutrons Isotopes of hydrogen These three isotopes play a central role in various fusion reactions.

11. Isotopes of carbon • Carbonhas 6protons and 6electrons(Z=6). Its outer shell contains 4 electrons, which determine the chemical properties of carbon. • The most common isotope of carbon has 6 neutrons, 12 nucleons. It is commonly labeled 12C (“C twelve”). • 14C is another isotope ofcarbon containing 8 neutrons,14 nucleons. • 14C is unstable and decays radioactively.

12. Half-life The decay of 14C is exponential (Lect. 4, Slides 5,6). After 6000 years, half of the 14C has decayed(= half-life).Afteranother 6000 years,one loses another half, and so on every 6000 years.

13. Carbon-dating question The 14C/12C ratio in a fossil bone is found to be ⅛ of the ratio in a living animal. What is the approximate ageofthefossil? • 6000 years • 18000 years • 32000 years • 48000 years Since the ratio has been reduced by a factor of ⅛ = ½½½ = (½)3, three half-lives have passed, i.e. 3 · 6000 years = 18000 years

14. Radioactive dating • Radioactive 14C is createdcontinuously by cosmicrays (next slide). • 14C oxidizes to CO2 and is converted by plants into organic matter. Particularly durable are wood and charcoal generated from wood. • Animals and humans eat plants and incorporate14C into the bones. • Decaying 14C is replenished as long as plants and animals are alive. • Once a plant or animal dies, its 14C content decreases and thereby starts the clock for radiocarbon dating. • By measuring the 14C/12C ratio of a sample from an archaeological site one can determine its age. (Willard Libby, 1969 Nobel Prize) • This can be done up to an age of about60000 years,when the14C concentration has been reduced by a factor of (½)10 =1/1024 .

15. Production of carbon 14C A cosmic ray proton shatters the nucleus of an atom in the upper atmosphere,creating neutrons n plus other debris. A 14N nucleus absorbs a neutron andemits aproton,becoming14C.

16. Concentration of 14C • A balance between theproduction and decay rates determines the equilibrium ratio: • Such an extremely low ratio of one part in a trillion requires a very sensitive detector which can detect single 14C atoms. • It helps to have a large number of C atoms from a macroscopic sample (compare Avogadro’s number, 1024).

17. Geological dating • For older specimens one uses isotopes with longer half-life, for example 235U (uranium). Its half-life is 0.7 billion years. • The oldest rocks on Earth have been dated this way. These are 4.4 billion years old. • Afocusedionbeamremovesasmallamountofmaterialfrom several spots on one of the tiny red zircon crystals.