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Asked in CBSE AIPMT 2009 · Q-value, decay and conservation laws
Let the substance emit x alpha particles and 2x beta particles.
Mass number: each α removes 4 nucleons and each β removes none, so A falls by 4x.
Atomic number: each α lowers Z by 2 and each β⁻ raises it by 1.
Net change in Z: -2x+2x=0, so the atomic number is unchanged.
Same Z with a different A is the definition of an isotope, so the daughter is an isotope of the parent.
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