Nuclear Chemistry and RadioactivityhardNUMERICAL

A highly unstable parent nucleus undergoes two successive emissions to directly form the stable isotNuclear Chemistry and Radioactivity Chemistry Question

Question

A highly unstable parent nucleus undergoes two successive $\beta^-$ emissions to directly form the stable isotope ${}_{7}^{14}N$. What was the original number of neutrons present in the initial parent nucleus?

Answer: 9

💡 Solution & Explanation

The reaction path is Parent $\xrightarrow{-2\beta^-} {}_{7}^{14}N$. Each $\beta^-$ emission increases the atomic number by 1 while keeping mass number constant. Thus, the parent must have an atomic number $Z = 7 - 2 = 5$. The mass number of the parent remains $14$. The parent nucleus is ${}_{5}^{14}X$. The number of neutrons in this parent nucleus is $A - Z = 14 - 5 = 9$.

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