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MHT CET 2020 (16 Oct, Shift 2) · Radioactive Decays: Alpha, Beta, Gamma

Radioactive Decays: Alpha, Beta, Gamma question from MHT CET 2020 (16 Oct, Shift 2)

Q20MHT CET 2020 · 16 OCT · SHIFT 2Medium

Radioactive Decays: Alpha, Beta, Gamma

A radioactive nucleus emits $4\alpha$ -particles and $7\beta$ -particles in succession. The ratio of number of neutrons of that of protons, is [ $A =$ mass number, $Z =$ atomic number]

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Answer: (b)

$4\alpha$ : $A' = A - 16$ , $\Delta Z = -8$ . $7\beta^-$ : $\Delta Z = +7$ .
Protons: $Z' = Z - 8 + 7 = Z - 1$ .
Neutrons: $A' - Z' = A - 16 - (Z - 1) = A - Z - 15$ .
Ratio $= \dfrac{A-Z-15}{Z-1}$ , so the answer is (b).

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