Table 44.3 shows that a Σ^0 decays into a Λ^0 and a photon. (a) Calculate the energy of the photon emitted in this decay, if the Λ^0 is at rest.

Verified step by step guidance

1. Identify the rest masses of the particles involved from a reliable source such as the Particle Data Group. Let the rest mass of Σ^0 be denoted as m_Σ and the rest mass of Λ^0 be denoted as m_Λ.
2. Use the conservation of energy principle. The initial energy is the rest mass energy of Σ^0, which is given by E_initial = m_Σc^2, where c is the speed of light.
3. Since the Λ^0 is at rest after the decay, its kinetic energy is zero. The total energy after the decay is the sum of the rest mass energy of Λ^0 and the energy of the photon, E_final = m_Λc^2 + E_photon.
4. Set up the equation for conservation of energy: m_Σc^2 = m_Λc^2 + E_photon. Solve this equation for E_photon, the energy of the photon.
5. E_photon = (m_Σ - m_Λ)c^2. This equation gives the energy of the photon emitted during the decay.

Key Concepts

Conservation of Energy

In any physical process, the total energy before the process must equal the total energy after the process. In particle decay, this principle dictates that the energy of the initial particle must be equal to the sum of the energies of the decay products, including any emitted photons. This concept is crucial for calculating the energy of the photon emitted during the decay of the Σ^0 particle.

Rest Mass Energy

The rest mass energy of a particle is given by Einstein's equation E=mc², where m is the rest mass and c is the speed of light. In the context of particle decay, the rest mass energies of the Σ^0 and Λ^0 particles must be considered to determine the energy available for the emitted photon. This energy contributes to the overall energy balance in the decay process.

Photon Energy

The energy of a photon is directly related to its frequency or wavelength, described by the equation E=hf, where h is Planck's constant and f is the frequency. In the decay process, the energy of the emitted photon can be calculated by considering the energy difference between the initial and final states of the system. Understanding this relationship is essential for determining the energy of the photon produced in the decay of the Σ^0.