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  4. An element X decays first by positron emission and then two α-particles are emitted in successive radioactive decay. If the product nucleus has mass number 227 and atomic number 89, the mass number and atomic number of element X are

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Q. An element X decays first by positron emission and then two α-particles are emitted in successive radioactive decay. If the product nucleus has mass number 227 and atomic number 89, the mass number and atomic number of element X are

Nuclei

Solution:

Let $A$ and $Z$ be mass number and atomic number of element $X$.
${ }_{ Z }^{ A } X \xrightarrow{\beta^{+}}{ }_{ Z -1}^{ A } Y \xrightarrow{{ }^{2 \alpha}}{ }_{ Z -5}^{ A -8} Y ^{\prime}$
Since the product nucleus has mass number 227 and atomic number 89 .
$\therefore A-8=227 \text { or } A=235 \text { and } Z-5=89 \text { or } Z=94$