rox 0.511 \\text{ MeV}$ (since it is the antiparticle of the electron, it has the same rest mass/energy)\n- **Photon ($\\gamma$):** Rest energy $= 0 \\text{ MeV}$ (since photons are massless)"},{"type":"text","order":2,"title":"Compare quantitative sums","content":"Let's calculate and compare the total rest energy before and after the decay:\n\n- **Parent rest energy:** \n $$E_{\\text{parent}} \\approx 135 \\text{ MeV}$$\n \n- **Combined products rest energy:** \n $$E_{\\text{products}} = 0.511 \\text{ MeV} + 0.511 \\text{ MeV} + 0 \\text{ MeV} \\approx 1.02 \\text{ MeV}$$"},{"type":"text","order":3,"title":"Formulate final comparison","content":"Comparing these values, the rest energy of the parent neutral pion ($135 \\text{ MeV}$) is significantly greater than the combined rest energies of its decay products ($1.02 \\text{ MeV}$):\n\n$$135 \\text{ MeV} \\gg 1.02 \\text{ MeV}$$\n\nThis excess rest energy is converted into kinetic energy carried away by the electron, positron, and photon."}]},{"id":"qualitative","label":"Qualitative Comparison","steps":[{"type":"text","order":0,"title":"Identify the decay particles","content":"First, let's identify the classification of each particle involved in the decay:\n$$\\pi^0 \\to \\text{e}^- + \\text{e}^+ + \\gamma$$\n\n- **Parent particle:** The neutral pion ($\\pi^0$) is a **meson** (a type of hadron made of quarks).\n- **Decay products:** \n - The electron ($\\text{e}^-$) and positron ($\\text{e}^+$) are **leptons** (fundamental particles with small mass).\n - The photon ($\\gamma$) is a **gauge boson** (a mediator of the electromagnetic force).","highlights":[{"text":"\\pi^0 \\to \\text{e}^- + \\text{e}^+ + \\gamma","location":"specification"}]},{"type":"text","order":1,"title":"Compare relative rest masses","content":"Next, let's look at the relative mass scales of these particle classes:\n\n- Mesons (like the pion) are significantly heavier than leptons (like the electron and positron).\n- Photons, as carriers of electromagnetic radiation, have **zero rest mass** (and thus $0\\text{ MeV}$ rest energy).\n\nLet's write down their approximate rest energies:\n- Neutral pion ($\\pi^0$): $\\approx 135 \\text{ MeV}$\n- Electron ($\\text{e}^-$) and positron ($\\text{e}^+$): $\\approx 0.51 \\text{ MeV}$ each\n- Photon ($\\gamma$): $0 \\text{ MeV}$"},{"type":"text","order":2,"title":"Analyze the energy balance","content":"Now we compare the combined rest energies of the decay products with the rest energy of the parent particle:\n\n$$\\text{Total rest energy of products} = 0.51\\text{ MeV} + 0.51\\text{ MeV} + 0\\text{ MeV} = 1.02\\text{ MeV}$$\n\nComparing this to the pion's rest energy ($135\\text{ MeV}$), we find that:\n$$135 \\text{ MeV} \\gg 1.02 \\text{ MeV}$$"},{"type":"text","order":3,"title":"Formulate the conclusion","content":"To secure full marks on this question, state your comparison clearly:\n1. The rest energy of the neutral pion ($\\approx 135 \\text{ MeV}$) is significantly greater than the rest energies of both the leptons ($\\approx 0.51 \\text{ MeV}$ each) and the photon ($0 \\text{ MeV}$). M1\n2. Therefore, the parent particle (the pion) has a much larger rest energy than the combined rest energies of all its decay products. A1\n\n*(Note: The remaining mass energy is converted into the kinetic energy of the products during the decay).*"}]}],"generatedAt":"2026-06-10T02:06:00.502Z","modelVersion":"gemini-3.5-flash","explanationVersion":"v2"},"options":[]},{"id":"fcf695af-bb82-4e1e-9a88-8d4eef6184e2","label":"d","content":"The decay of the neutral pion meson leads to the production of further gamma photons. Explain why.","markscheme":"- Identifies the positron ($\\text{e}^+$) as antimatter B1\n- Explains that the positron will meet an electron in the surrounding matter and undergo annihilation M1\n- States that this annihilation process converts mass to energy, producing a pair of gamma-ray photons A1","marks":3,"order":3,"markingRubric":null,"explanation":{"methods":[{"id":"direct_exp

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Question 12

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Particles

Question 12

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