Question

(a) Is the decay n→p+β−+ve‾n\rightarrow p+\$$beta^{-}$$+\overline{v_{e}} energetically possible? If not, explain why not. If so, calculate the total energy released.(b) Is the decay n→p+β++ve‾n\rightarrow p+\$$beta^{+}$$+\overline{v_{e}} energetically possible? If not, explain why not. If so, calculate the total energy released.

Accepted Answer

Step 1: Understand the problem. The question involves analyzing two decay processes: (a) neutron decay into a proton, beta-minus particle (b⁻), and antineutrino (νₑ), and (b) proton decay into a neutron, beta-plus particle (b⁺), and neutrino (νₑ). We need to determine if these decays are energetically possible and calculate the energy released if they are. Step 2: Recall the concept of mass-energy equivalence. The energy released in a decay process is determined by the difference in mass between the initial particle and the sum of the masses of the decay products. Use the equation ΔE = Δm × c², where Δm is the mass difference and c is the speed of light. Step 3: For part (a), compare the mass of the neutron (mₙ) with the combined mass of the proton (mₚ), beta-minus particle (m_b⁻), and antineutrino (m_νₑ). Note that the antineutrino has negligible mass. If mₙ \u003e mₚ + m_b⁻, the decay is energetically possible, and the energy released is ΔE = (mₙ - mₚ - m_b⁻) × c². Step 4: For part (b), compare the mass of the proton (mₚ) with the combined mass of the neutron (mₙ), beta-plus particle (m_b⁺), and neutrino (m_νₑ). Again, the neutrino has negligible mass. If mₚ \u003e mₙ + m_b⁺, the decay is energetically possible, and the energy released is ΔE = (mₚ - mₙ - m_b⁺) × c². Step 5: Use known values for the masses of the neutron, proton, beta-minus particle, and beta-plus particle from a reliable source (e.g., a physics textbook or database). Plug these values into the equations derived in steps 3 and 4 to determine whether each decay is energetically possible and calculate the energy released if applicable.

(a) Is the decay $n \to p + β^{-} + \overline{v_{e}}$ energetically possible? If not, explain why not. If so, calculate the total energy released.
(b) Is the decay $n \to p + β^{+} + \overline{v_{e}}$ energetically possible? If not, explain why not. If so, calculate the total energy released.

비슷한 문제에 대한 검증된 영상 답변:

주요 개념

Conservation of Energy

Mass-Energy Equivalence

Beta Decay