13.2.3 & 13.2.4 Nuclear Physics

13.2.3 Describe one piece of evidence for the existence of nuclear energy levels.

For example, alpha (α) particles produced by the decay of a nucleus have discrete energies; gamma‑ray (γ-ray) spectra are discrete. Students should appreciate that the nucleus, like the atom, is a quantum system and, as such, has discrete energy levels.



The energies of both alpha and gamma are discrete (quantized) and have only certain values. Since these discrete energies come from the nucleus, it must follow that the nucleus has discrete nuclear energy levels. The graph below shows this property of alpha and is adapted from Heinemann HL Physics book by Chris Hamper.

13.2.4 Describe β+ decay, including the existence of the neutrino.

Students should know that β energy spectra are continuous, and that the neutrino was postulated to account for these spectra.


When energy calculations were done with beta emissions, scientists observed that the beta particles had less kinetic energy than expected. This opposed the law of conservation of energy (and in fact, scientists were so puzzled by this problem that they started to question the law of conservation of energy itself). In 1930, Wolfgang Pauli postulated that there was a virtually undetectable particle that therefore carried away this missing kinetic energy and momentum. This particle was named a 'neutrino'.


A neutrino is electrically neutral, has a very very small mass and travels at the speed of light.


In positron decay, a proton within the nucleus decays into a neutron and a positron (antimatter version of an electron--its antiparticle, when the two collide, they annihilate each other) is emitted. The equation for is is shown below (extracted from IB Physics Study Guides by Tim Kirk):

 Because of neutrinos and anti-neutrinos, beta emission forms a continuous spectrum. This is shown below (graph adapted from Heinemann HL Physics book by Chris Hamper).