Energy from Nuclei

In analogy with combustion,
         "Heat generated by molecule burning
         to more stable end products."
and with Einstein's insight --E = mc2 -- energy generated by less stable nucleus (atom) "burning" into more stable ones.

What then is the binding energy of nucleus? That is, what are the masses of the nuclei?

Weighting the nucleus -- nuclear chemistry

Definitions -- what is

Nuclear Landscape -- Isotope Zoo

Prominent features. Th-232 1010; U-234 106/4; U-235 0.7 109; U-238 4.5 109yr.

Binding Energy of Nuclei

Magnitude of Binding energy of nucleus is difference between the mass of the nucleus and that of constituent nucleons -- just like chemistry.

Binding energy per nucleon, most bound lie lowest.
(Binding energy is positive; plot emphasizes stability.)
Leftmost dip:
   4He = α + 2 e-
56Fe: most bound
To left: nuclei
   merge: fusion
To right: nuclei
   split: fission

Units: u (amu or atomic mass unit) = 1.6606 10-27 kg.
Conspiracy. Mass of 168O = 16 u.
Conversion: u = 931 MeV = 0.149 nJ=149.0 pJ;
      neutron = 1.008669 u, proton = 1.007276 u.
Ref: Nulear Mass Table

Fission: Energy & Decay Products

92-U-235 +n = 56-Ba-141 +
36-Kr-92 + 2 n

ElementEnergyunit
U-235235.0439u
Ba-141-140.9144u
Kr-92-91.9262u
2 n (1.0078)-2.0156u
  excess 0.1877u
174.7MeV
28.0pJ

On a mass basis (235 1.66 10-27 = 0.39 10-24 kg)
  235U fission produces 72 TJ/kg.
  Methane combustion yields 50 MJ/kg. (TNT: 4 MJ/kg)
  Fission is million times more energetic!

23592U plus slow neutron has other fission reactions. See text for example and distribution. But the effectiveness of fission persists.

Most neutrons are prompt; 0.7% delayed ms→min.

Chain Reactions and Fission Products

Average number of neutron released is 2.4. That there is more than one neutron permits a chair reaction.

U-235 + n chain reaction

1. Stable energy requires neutrons cooled & most absorbed.
2. Reaction products in excited states that decay by emitting α (He-4 nucleus), β (both + & - electrons) and γ (MeV xrays).
U-235 fission product
distribution penetration of
alpha, beta, gamma Relative penetration of α, β & γ.
Distribution 235U fission fragments. Most radioactive; some long lifetimes.

Heavy Element Synthesis
(beyond iron -- most stable element)>

Slow neutron capture

To get higher Z, we can use repeated neutron capture until eventually one of the neutron decays and Z increase (due to new proton.) That can only happen if neutron capture is much slower than beta decay (neutron -> proton + electron). With successive neutron capture, rate increase until it exceeds beta decay rate.
Fe(56) -> Fe(57) -> Fe(58) -> Fe(59) -> Co(59)

This slow process works until Pb(208) is reached when no higher elements are stable enough for slow capture to work. Nuclear physics has worked hard to calculate these processes and in the effort found interesting aspects, the most relevant here is that the process work best is old, mostly burnt-out stars carbon-oxygen cores (not H-He ones). They are supported by helium burning in a shell around the core that serves as good neutron source. Moreover the these stars convects newly formed higher Z elements to the surface where they may released by stellar wind or supernova explosion.

Fast neutron capture

This process is still being worked on and I keep seeing new papers refining the process. Each, of course, claims it is the solution. All involve intense neutron sources so a target element "absorbs" neutrons until it reaches some special value such as "magic number" of neutrons and then coverts to higher Z element. Stay tuned.

Move on Safe Power Generatation



To cite this page:
Energy from Nuclei
<http://www.physics.ohio-state.edu/~wilkins/energy/Resources/Lectures/nucenergy.html>
[Friday, 15-Dec-2017 05:25:08 EST]
Edited by: wilkins@mps.ohio-state.edu on Monday, 25-Sep-2017 13:37:02 EDT