Q25Q In one type of nuclear radioacti... [FREE SOLUTION]

Chapter 7: Q25Q (page 170)

In one type of nuclear radioactive decay, an electron and a recoil nucleus are emitted but often do not separate along the same line. Use conservation of momentum in two dimensions to explain why this implies the emission of at least one other particle (it came to be called a 鈥渘eutrino鈥�.

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An electron and a recoil nucleus are emitted, but they often do not separate along the same line because their momenta lie along different lines.

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Conservation of momentum condition for a two-particle decay

According to the conservation of momentum principle, the momentum of an isolated system remains conserved.

Using this principle, you can say that the two elements obtained as decay products have an equal magnitude of momentum but in opposite directions.This conserves the momentum of the two-particle radioactive emission

Conservation of momentum by a third particle neutrino

In a case of nuclear radioactive decay, an electron and a recoil nucleus are emitted, but often they do not separate along the same line. By the principle of conservation of energy, the momenta of the decay products should lie along a line. If the momenta of the recoil nucleus and the electron do not lie along a plane, some other particle will have to decay to conserve the momentum.

Consider if a particle is decayed along the positive x-axis, then another particle must decaying along the negative x-axis to conserve the momentum as the initial momentum of the system is zero. But this does not happen in nuclear decay; the decay of particles is not in line. That is why a third particle, often called a neutrino, is emitted to conserve momentum.