Question

Decay of Particles Consider the decay of a massive particle of mass M into two massive particles of masses m₁ and m₂. The decaying particle is called the parent, while the product particles are called the daughters. Working in the rest frame of the decaying particle, and using conservation of momentum and energy, (a (8) Express the momentum, p, of each of the two daughter particles in terms of the masses of the parent particle. (b) (4) Express the energy of each particle, E₁ , E₂, in terms of the masses and total energy of the parent particle.

Answer 1

In the decay of a parent particle into two daughter particles at rest, the momentum of each daughter is equal and opposite to conserve linear momentum, and their energies are derived from the conservation of energy principle based on their masses and the total energy of the parent particle.

Step-by-step explanation:

The decay of a particle into two smaller particles can be analyzed using conservation of momentum and energy. If a parent nucleus is at rest when it decays, its momentum is zero, and thus the daughters must have equal and opposite momentum to conserve linear momentum. Using the conservation of energy, we know that the total energy of the daughter particles must be equal to the rest energy of the parent particle (assuming no external forces are acting on the system). The momentum p of each daughter particle can be found using the relativistic relationship between energy, mass, and momentum. Assuming the parent particle decays into two daughter particles at rest, the momentum of each daughter particle is given by the formula p = √((Etotal^2/c^2) - (m_1 + m_2)^2), where Etotal is the total energy of the parent particle and c is the speed of light in a vacuum. The energies E1 and E2 of the daughter particles can then be expressed as E1 = √((pc)^2 + (m1c^2)^2) and E2 = √((pc)^2 + (m2c^2)^2) respectively.