Alpha And Beta Decay

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A uranium-238 nucleus with atomic number 92 first emits an alpha particle and subsequently undergoes two successive beta-minus decays. What is the atomic number and mass number of the final daughter nucleus produced?

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In alpha decay a nucleus loses an alpha particle ($^4_2	ext{He}$), reducing its mass number by 4 and its atomic number by 2. In beta-minus decay a neutron converts to a proton, leaving the mass number unchanged while raising the atomic number by 1. Starting from $^{238}_{92}	ext{U}$, the alpha emission gives mass $238 - 4 = 234$ and charge $92 - 2 = 90$, producing $^{234}_{90}	ext{Th}$. The two subsequent beta-minus decays each add 1 to the atomic number without altering the mass: $90 	o 91 	o 92$, while mass stays at 234. The final nucleus therefore has mass number 234 and atomic number 92. The option mass 234, atomic number 90 stops after the alpha step and forgets the beta decays. The option mass 230, atomic number 88 wrongly applies two alpha decays. The option mass 234, atomic number 91 includes only one beta decay. The emitted beta-minus particle is an electron created at the instant a neutron transforms into a proton, which conserves the overall electric charge of the system. This follows the NCERT displacement laws. A plausibility check confirms mass number is conserved through beta decay and only the alpha step removes nucleons, consistent with the final mass of 234.

Alpha And Beta Decay

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