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An excited heavy nucleus ZAX{}_{Z}^{A}\mathrm{X} emits radiations in the following sequence: ZAXZ2A4D1Z1A4D2Z3A8D3Z4A8D4Z4A8D5{}_{Z}^{A}\mathrm{X} \rightarrow {}_{Z-2}^{A-4}\mathrm{D}_1 \rightarrow {}_{Z-1}^{A-4}\mathrm{D}_2 \rightarrow {}_{Z-3}^{A-8}\mathrm{D}_3 \rightarrow {}_{Z-4}^{A-8}\mathrm{D}_4 \rightarrow {}_{Z-4}^{A-8}\mathrm{D}_5 where Z,AZ, A are the atomic and mass number of element X\mathrm{X}, respectively. The possible emitted particles or radiations in the sequence, respectively are:

A

e+,α,e,α,γe^+, \alpha, e^-, \alpha, \gamma

B

e,α,e+,α,γe^-, \alpha, e^+, \alpha, \gamma

C

α,e,α,e+,γ\alpha, e^-, \alpha, e^+, \gamma

D

α,e+,α,e,γ\alpha, e^+, \alpha, e^-, \gamma

Step-by-Step Solution

  1. Step 1: ZAXZ2A4D1{}_{Z}^{A}\mathrm{X} \rightarrow {}_{Z-2}^{A-4}\mathrm{D}_1. Mass number decreases by 4 (AA4A \to A-4) and atomic number decreases by 2 (ZZ2Z \to Z-2). This corresponds to the emission of an \alpha particle (α\alpha, 24He{}_{2}^{4}\mathrm{He}) .
  2. Step 2: Z2A4D1Z1A4D2{}_{Z-2}^{A-4}\mathrm{D}_1 \rightarrow {}_{Z-1}^{A-4}\mathrm{D}_2. Mass number remains unchanged (A4A4A-4 \to A-4), but atomic number increases by 1 ((Z2)(Z1)(Z-2) \to (Z-1)). This corresponds to the emission of a beta-minus particle (ee^-, 10e{}_{-1}^{0}e) .
  3. Step 3: Z1A4D2Z3A8D3{}_{Z-1}^{A-4}\mathrm{D}_2 \rightarrow {}_{Z-3}^{A-8}\mathrm{D}_3. Mass number decreases by 4 ((A4)(A8)(A-4) \to (A-8)) and atomic number decreases by 2 ((Z1)(Z3)(Z-1) \to (Z-3)). This corresponds to the emission of another \alpha particle (α\alpha, 24He{}_{2}^{4}\mathrm{He}).
  4. Step 4: Z3A8D3Z4A8D4{}_{Z-3}^{A-8}\mathrm{D}_3 \rightarrow {}_{Z-4}^{A-8}\mathrm{D}_4. Mass number remains unchanged, but atomic number decreases by 1 ((Z3)(Z4)(Z-3) \to (Z-4)). This corresponds to the emission of a positron (e+e^+, +10e{}_{+1}^{0}e or β+\beta^+) .
  5. Step 5: Z4A8D4Z4A8D5{}_{Z-4}^{A-8}\mathrm{D}_4 \rightarrow {}_{Z-4}^{A-8}\mathrm{D}_5. Both mass number and atomic number remain unchanged. This indicates a transition from an excited state to a lower energy state via the emission of a \gamma ray (γ\gamma) .

Sequence: α,e,α,e+,γ\alpha, e^-, \alpha, e^+, \gamma.

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