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Energy Conservation in Beta Decay – Discovery of the Neutrino

Beta-decay (β-decay) is a type of radioactive decay in which a beta particle and a respective neutrino are emitted from an atomic nucleus. Beta radiation consists of high-energy beta particles. High-speed electrons or positrons are emitted during beta decay. By beta decay emission, a neutron is transformed into a proton by the emission of an electron. Conversely, a proton is converted into a neutron by the emission of a positron, thus changing the nuclide type.

beta decay
Beta-decay of C-14 nucleus.

Discovery of the Neutrino

The study of beta decay provided the first physical evidence for the existence of the neutrino. The discovery of the neutrino is based on the law of conservation of energy during the process of beta decay.

The resulting particle (alpha particle or photon) has a narrow energy distribution in alpha and gamma decay. The particle carries the energy from the difference between the initial and final nuclear states. For example, in the case of alpha decay, when a parent nucleus breaks down spontaneously to yield a daughter nucleus and an alpha particle, the sum of the mass of the two products does not quite equal the mass of the original nucleus (see Mass Defect). As a result of the law of conservation of energy, this difference appears in the form of the kinetic energy of the alpha particle. Since the same particles appear as products at every breakdown of a particular parent nucleus, the mass difference should always be the same, and the kinetic energy of the alpha particles should also always be the same. In other words, the beam of alpha particles should be monoenergetic.

It was expected that the same considerations would hold for a parent nucleus breaking down to a daughter nucleus and a beta particle. Because only the electron and the recoiling daughter nucleus were observed beta decay, the process was initially assumed to be a two-body process, very much like alpha decay. It would seem reasonable to suppose that the beta particles would also form a monoenergetic beam.

To demonstrate the energetics of two-body beta decay, consider the beta decay in which an electron is emitted and the parent nucleus rest. Conservation of energy requires:

conservation-of-energy-beta-decay

Since the electron is a much lighter particle, it was expected that it would carry away most of the released energy, which would have a unique value Te-.

Energy spectrum of beta decay
The shape of this energy curve depends on what fraction of the reaction energy (Q value-the amount of energy released by the reaction) is carried by the electron or neutrino.

But the reality was different. However, the spectrum of beta particles measured by Lise Meitner and Otto Hahn in 1911 and by Jean Danysz in 1913 showed multiple lines on a diffuse background. Moreover, virtually all of the emitted beta particles have energies below predicted by energy conservation in two-body decays. The electrons emitted in beta decay have a continuous rather than a discrete spectrum that appeared to contradict conservation of energy, under the then-current assumption that beta decay is the simple emission of an electron from a nucleus. When this was first observed, it appeared to threaten the survival of one of the most important conservation laws in physics!

To account for this energy release, Pauli proposed (in 1931) that there was emitted in the decay process another particle, later named by Fermi the neutrino. It was clear, this particle must be highly penetrating and that the conservation of electric charge requires the neutrino to be electrically neutral. This would explain why it was so hard to detect this particle. The term neutrino comes from Italian, meaning “little neutral one,” and neutrinos are denoted by the Greek letter ν (nu). In the process of beta decay, the neutrino carries the missing energy, and also, in this process, the law of conservation of energy remains valid.

 
References:
Nuclear and Reactor Physics:
  1. J. R. Lamarsh, Introduction to Nuclear Reactor Theory, 2nd ed., Addison-Wesley, Reading, MA (1983).
  2. J. R. Lamarsh, A. J. Baratta, Introduction to Nuclear Engineering, 3d ed., Prentice-Hall, 2001, ISBN: 0-201-82498-1.
  3. W. M. Stacey, Nuclear Reactor Physics, John Wiley & Sons, 2001, ISBN: 0- 471-39127-1.
  4. Glasstone, Sesonske. Nuclear Reactor Engineering: Reactor Systems Engineering, Springer; 4th edition, 1994, ISBN: 978-0412985317
  5. W.S.C. Williams. Nuclear and Particle Physics. Clarendon Press; 1 edition, 1991, ISBN: 978-0198520467
  6. Kenneth S. Krane. Introductory Nuclear Physics, 3rd Edition, Wiley, 1987, ISBN: 978-0471805533
  7. G.R.Keepin. Physics of Nuclear Kinetics. Addison-Wesley Pub. Co; 1st edition, 1965
  8. Robert Reed Burn, Introduction to Nuclear Reactor Operation, 1988.
  9. U.S. Department of Energy, Nuclear Physics and Reactor Theory. DOE Fundamentals Handbook, Volume 1 and 2. January 1993.

Advanced Reactor Physics:

  1. K. O. Ott, W. A. Bezella, Introductory Nuclear Reactor Statics, American Nuclear Society, Revised edition (1989), 1989, ISBN: 0-894-48033-2.
  2. K. O. Ott, R. J. Neuhold, Introductory Nuclear Reactor Dynamics, American Nuclear Society, 1985, ISBN: 0-894-48029-4.
  3. D. L. Hetrick, Dynamics of Nuclear Reactors, American Nuclear Society, 1993, ISBN: 0-894-48453-2. 
  4. E. E. Lewis, W. F. Miller, Computational Methods of Neutron Transport, American Nuclear Society, 1993, ISBN: 0-894-48452-4.

See above:

Conservation of Energy