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Question
An element X has the symbol 84X202. It emits an alpha-particle and then a beta-particle. The final nucleus is bYa. Find a and b.
Solution
\[\ce{_{Z-2}X^{A-4} ->_{Z-1}Y^{A-4} + _-1e^0}\] (β-emission)
\[\ce{_84X^202->_82X1^198 + _2He^4}\] (α- particles)
\[\ce{_82X1^198 -> _83Y^198 + _-1e^0}\] (β-emission)
\[\ce{_bY^a = _83Y^198}\]
∴ a = 198 and b = 83
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