Observations show that if there were no neutrino, βdecay would violate conservation of momentum,

step 1 Here is the decay process of the helium atom, which is shown as follows. Helium decay into lithi

Observations show that if there were no neutrino, βdecay...

Observations show that if there were no neutrino, $\beta$ decay would violate conservation of momentum, as well as energy. For example, in a decay of ${ }^{6} \mathrm{He}$ at rest, the two final charged particles were observed with momenta as shown in Fig. 17.32. (a) Show that this decay would violate conservation of momentum if there were no neutrino involved. (b) Assuming that a neutrino is ejected and that total momentum is conserved, calculate the momentum (magnitude and direction) of the unobserved neutrino. (c) Assuming conservation of energy, find the neutrino's energy. (d) Show that your answers in parts (b) and (c) are consistent with the neutrino's having zero rest mass (within the accuracy of the given numbers).

Observations show that if there were no neutrino, $\beta$ decay would violate conservation of momentum, as well as energy. For example, in a decay of ${ }^{6} \mathrm{He}$ at rest, the two final charged particles were observed with momenta as shown in Fig. 17.32. (a) Show that this decay would violate conservation of momentum if there were no neutrino involved. (b) Assuming that a neutrino is ejected and that total momentum is conserved, calculate the momentum (magnitude and direction) of the unobserved neutrino. (c) Assuming conservation of energy, find the neutrino's energy.
(d) Show that your answers in parts (b) and (c) are consistent with the neutrino's having zero rest mass (within the accuracy of the given numbers).

Key Concepts

Beta Decay

Beta decay is a type of radioactive decay in which a beta particle (an electron or positron) is emitted from a nucleus. It involves the transformation of a neutron into a proton (or vice versa) along with the emission of a beta particle and another neutral particle (the neutrino or antineutrino). This process is an important example of weak nuclear interactions and illustrates the role of subatomic particles in nuclear transformations.

Conservation of Momentum

Conservation of momentum is a fundamental principle in physics stating that the total momentum of an isolated system remains constant if no external forces act upon it. In particle decays, this means that the vector sum of the momenta of all products must equal the momentum of the original particle. This principle is crucial in analyzing decay processes and can reveal missing momentum-carrying particles when experimental observations do not account for momentum balance.

Conservation of Energy

Conservation of energy is a fundamental law which asserts that the total energy of an isolated system remains constant over time. In the context of nuclear decay, both kinetic energy and the rest mass energy of the particles involved must be accounted for. Ensuring that energy is conserved in decay processes provides constraints on the allowed energies of emitted particles and helps in predicting or reconciling the presence of particles that may be undetectable directly.

Neutrino in Beta Decay

The neutrino’s inclusion in beta decay is critical to satisfy both energy and momentum conservation. Originally, the observed continuous energy spectrum of beta particles led to the proposal of the neutrino, a nearly massless and chargeless particle, to account for the missing energy and momentum. This idea helped resolve the puzzle where, without its involvement, conservation laws appeared violated, and it remains a fundamental aspect of our understanding of weak interactions.

Zero Rest Mass Hypothesis

The zero rest mass hypothesis for neutrinos (or being extremely small mass) underpins many calculations in beta decay processes. When neutrinos are assumed to be massless, their energy is directly proportional to their momentum. This assumption simplifies the analysis of their kinematic properties, such as computing their momentum and energy from conservation laws, and plays a key role in validating the consistency of theoretical predictions with experimental observations.

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