The nucleus is 0 decays by electron capture. The nuclear...

The nucleus is 0 decays by electron capture. The nuclear reaction is written $$ _{8}^{15} \mathrm{O}+\mathrm{e}^{-} \rightarrow_{7}^{15} \mathrm{N}+v $$ (a) Write the process going on for a single particle within the nucleus. (b) Write the decay process referring to neutral atoms. (c) Determine the cnergy of the neutrino. Dis- regard the daughter's recoil.

The nucleus is 0 decays by electron capture. The nuclear reaction is written
$$
_{8}^{15} \mathrm{O}+\mathrm{e}^{-} \rightarrow_{7}^{15} \mathrm{N}+v
$$
(a) Write the process going on for a single particle within the nucleus. (b) Write the decay process referring to neutral atoms. (c) Determine the cnergy of the neutrino. Dis- regard the daughter's recoil.

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Key Concepts

Electron Capture

Electron capture is a mode of radioactive decay in which a proton-rich nucleus absorbs one of its own atomic electrons, typically from an inner orbital, converting a proton into a neutron and emitting a neutrino. This process is mediated by the weak nuclear force and changes the element into one with one fewer proton.

Atomic Versus Nuclear Decay Processes

While electron capture occurs at the nuclear level—where a proton transforms into a neutron—the full decay process of a neutral atom must account for the rearrangement of the electron cloud. This means that when considering neutral atoms, the process includes the capture of an electron from an orbital and the resulting change in the chemical identity of the atom, with the appropriate adjustment in electron count.

Energy Conservation and Q-value

In nuclear decays such as electron capture, the difference in mass-energy between the initial and final states (the Q-value) is distributed among the decay products; in this case, it largely appears as the kinetic energy of the emitted neutrino (when neglecting any recoil of the daughter nucleus). Accurate determination of the neutrino energy involves applying conservation of energy to equate the mass differences to the kinetic energies released in the decay.

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