To solve the problem of identifying the correct product of the radioactive decay of a radon atom given the provided decay process, we'll follow these steps:
1. Identify the given decay reaction:
[tex]\[
\,_{86}^{198} \text{Rn} \longrightarrow \,_{2}^{4} \text{He} + \,_{Z}^{A} \text{X}
\][/tex]
where [tex]\(_{86}^{198} \text{Rn}\)[/tex] is the radon atom and [tex]\(_{2}^{4} \text{He}\)[/tex] represents the helium nucleus (alpha particle). The unknown product is denoted by [tex]\(_{Z}^{A} \text{X}\)[/tex].
2. Apply the conservation of mass number:
The mass number (A) is conserved in the reaction. The initial mass number of radon is 198, and the mass number of the emitted helium nucleus is 4. Therefore,
[tex]\[
A_{\text{unknown}} = 198 - 4 = 194
\][/tex]
So, the mass number of the unknown product is 194.
3. Apply the conservation of atomic number:
The atomic number (Z) is also conserved in the reaction. The initial atomic number of radon is 86, and the atomic number of the emitted helium nucleus is 2. Therefore,
[tex]\[
Z_{\text{unknown}} = 86 - 2 = 84
\][/tex]
So, the atomic number of the unknown product is 84.
4. Identify the element with atomic number 84:
Using a periodic table, we find that the element with atomic number 84 is Polonium (Po).
Thus, the product of this radioactive decay process is Polonium with a mass number of 194. The correct symbol to complete the decay process is:
[tex]\[
\,_{86}^{198} \text{Rn} \longrightarrow \,_{2}^{4} \text{He} + \,_{84}^{194} \text{Po}
\][/tex]
