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A nucleus ${}_{Z}X^{A}$ emits 9α-particles and $5 β$ particle. The ratio of total protons and neutrons in the final nucleus is

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$\frac{{(Z - 13)}}{{(A - Z - 13)}}$

$\frac{{Z - 13}}{{(A - Z - 23)}}$

$\frac{{(Z - 18)}}{{(A - 36)}}$

$\frac{{(Z - 13)}}{{(A - 36)}}$

answer is A.

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Detailed Solution

_Z{X^A}\,\xrightarrow{{9\alpha ,}}{\,_{Z - 18}}{X^{A - 36}}\xrightarrow{{5\beta }}{\,_{Z - 13}}{X^{A - 36}}

Number of protons P = (Z - 13)

Number of neutrons N = (A – 36) – (Z – 13) = (A – Z – 23)

\therefore \frac{P}{N} = \frac{{(Z - 13)}}{{(A - Z - 23)}}

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