A radioactive nucleus ^A_ZX undergoes spontaneous decay in the sequence ^A_ZX → _Z-1B → _Z-3C → _Z-2D, where Z is the atomic number of element X. The possible decay particles in the sequence are

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(3) β⁺, α, β⁻. Track the atomic number alone; the sequence gives it at every stage. Step 1: Z → Z-1, a fall of one unit. A proton has become a neutron, so a positron is emitted: β⁺. Step 2: Z-1 → Z-3, a fall of two units. Of the particles offered, only an α-particle (charge +2e) lowers Z by 2. That is α decay. Step 3: Z-3 → Z-2, a rise of one unit. A neutron has become a proton: β⁻. The order is β⁺, α, β⁻.

A radioactive nucleus ^A_ZX undergoes spontaneous decay in the sequence ^A_ZX → _Z-1B → _Z-3C → _Z-2D, where Z is the atomic number of element X. The possible decay particles in the sequence are

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