Nuclear 2 Fission and Fusion
History 1896: Becquerel discovers radioactivity 1898: Marie & Pierre Curie discover radium 1911: Rutherford discovers nucleus 1932: Chadwick discovers neutrons 1933: Hitler becomes Chancellor 1934: Joliot-Curies and Fermi induce artificial radioactivity via alphas and neutrons 1938: Hahn and Strassman show that Fermi had observed fission.
More History 1938: Meitner and Frisch describe fission theoretically, and show large amounts of energy can be released 1938: Szilard confirms energy release experimentally, and demonstrates possibility of nuclear chain reaction. 1938: Nazis invade Czecholslovakia 1939: Nazis invade Poland 1939: Einstein-Szilard letter to Roosevelt
Energy of the nucleus Energy and mass are equivalent according to E = mc 2 c = 300,000 km/s = speed of light Energy (nucleus: Z protons and N neutrons) = Z m p c 2 + N m n c 2 - Binding Energy (N,Z) Binding Energy (N,Z) = BE ( A Chemical Symbol) Binding Energy : energy required to completely decompose nucleus into its constituents Determines the possibility (energy) of fission or fusion
Binding energy per nucleon BE/A Fusion region Fission region Number of nucleons in nucleus (A)
Key Facts Nuclei want to be in states of lowest energy. Lowest energy means largest binding energy (because of the minus sign in definition of binding energy). Nuclei in the middle have the highest binding energy per nucleon. Lighter nuclei go to lower energy states by combining (fusion) Heaviest nuclei can lower their energy by coming apart (fission). Nuclei around Iron are most stable.
Fission of U-235 Atomic numbers of fission products are distributed among all possibilities. Split into exact halves is not most likely process.
Fission energy Energy considerations make fission possible: Heavy nucleus two smaller nuclei Example: split 240 Pu into two 120 Ag nuclei 240 94Pu 146 120 47 Ag 73 + 120 47 Ag 73 + fission energy Energy balance : Look up : Initially 94 m p c 2 + 146 m n c 2-1813 MeV = BE( 240 Pu) = 1813 MeV BE( 120 Ag) = 1008 MeV Finally 2 x (47 m p c 2 + 73 m n c 2-1008 MeV) + fission energy Solve for fission energy : fission energy = 203 MeV (enormous)
Fission Fission is nuclear energy from splitting heavy nuclei Spontaneous fission is very improbable Fission can be induced! 1934 Fermi: n + U elements heavier than U (transuranics) 1938 Hahn & Strassmann n + 235 U Barium???!!!??? 1938/9Frisch & Meitner understand that fission occurs! Two nuclei yield fission with high probability (are fissile) when bombarded with low energy neutrons 235 U occurs naturally but in small amounts 239 Pu not available before 1940!!
Fusion energy Fusion occurs in the sun Hydrogen or thermonuclear bomb Example of fusion reaction : 2 H+ 2 H 3 He + n + fusion energy 2 H contains 1 p and 1 n and is called a deuteron Look up : BE ( 2 H) = 2.2245 MeV BE ( 3 He) = 7.718 MeV Energy balance : Initially 2 x ( m p c 2 + m n c 2-2.2245 MeV) = Finally 2 m p c 2 + m n c 2-7.718 MeV + m n c 2 + fusion energy Solve for fusion energy : fusion energy = 3.269 MeV (a lot...)
Picture of a fusion reaction Deuterium and Tritium are isotopes of Hydrogen. D has 1 neutron; T has 2. Final result is He-4 + a neutron.
Self-sustaining Nuclear Reactions Neutrons induce fission. More neutrons can lead to more fission events, leading to more neutrons, and so on... This is known as a chain reaction
Another view of a chain reaction http://lectureonline.cl.msu.edu/~mmp/applist/chain/chain.htm
More on chain reactions Self-sustaining chain reaction : Each fission event must produce 1 or more free neutrons : average 2.5 for 235 U & 3 for 239 Pu One or more of these n must induce another fission event Fate of n : - leaves the sample make sample larger use n reflectors minimize surface (sphere) compress sample (bombs) - n may be absorbed purer 235 U (enrichment)
Still more... Naturally occurring Uranium : 99.3 % 238 U and 0.7 % 235 U Weapons-grade uranium enriched to 95 % Reactor-grade uranium enriched up to 4 % Capability of sample to sustain chain reaction characterized by k multiplication factor Example: - throw 100 n in sample and wait 10-8 s for their fate - then check how many free n there are : x - k = x / 100 What will k be for a -bomb? -reactor? As large as possible 1
and more... k = 1 critical point between a reaction that grows or dies out So mass of fissile material with k 1 is called critical mass (actually depends on geometry of material- more later) Time step for next fission events : n from fission fast neutrons with kinetic energy of about 1 MeV 1 MeV = 0.5 m n v 2 = kinetic energy m n c 2 = 939 MeV = 0.5 m n c 2 v 2 / c 2 So v 2 / c 2 = 2 / 939 or v = (2/939) * c = 1.4 10 7 m/s Assume n in pure 235 U sphere with 0.1 m radius will induce fission within t = 0.1 m / v 10-8 s So time step is only about 10-8 s!!
Growth of released energy Assume half of the n lead to fission (180 MeV) N generation Time (μs) # neutrons Energy (MeV) 0th 0.00 1 0 1st 0.01 2.7 245 2nd 0.02 7.4 910 3rd 0.03 20.0 2720 10th 0.1 2.2 x 10 4 3.1 x 10 6 20th 0.2 4.9 x 10 8 6.9 x 10 10 50th 0.50 5.2 x 10 21 7.4 x 10 23 56th 0.56 2.1 x 10 24 3.0 x 10 26 57th 0.57 5.7 x 10 24 8.1 x 10 26 Exponential growth! 1 kiloton TNT = 2.6 x 10 25 MeV
How much fissionable material is needed? Pure 235 U critical mass 20 kgsize of softball Pure 239 Pu critical mass 10 kgsize of baseball Still, it is difficult to make bombs...