Let's solve the problem step by step to identify the resulting atom after the radioactive decay.
1. Understand the given equation:
[tex]\[
{ }_{83}^{209} Bi \rightarrow \_+{ }_2^4 He
\][/tex]
Here, [tex]\({ }_{83}^{209} Bi\)[/tex] is the initial atom that undergoes decay, and [tex]\({ }_2^4 He\)[/tex] is an alpha particle emitted during the decay process.
2. Identify the properties of the alpha particle:
An alpha particle has:
- An atomic number (protons) of 2.
- A mass number (protons + neutrons) of 4.
3. Determine the atomic number of the resulting atom:
The initial atomic number of [tex]\({ }_{83}^{209} Bi\)[/tex] is 83. During the decay, the atom loses 2 protons because it emits an alpha particle.
[tex]\[
\text{Resulting Atomic Number} = 83 - 2 = 81
\][/tex]
4. Determine the mass number of the resulting atom:
The initial mass number of [tex]\({ }_{83}^{209} Bi\)[/tex] is 209. During the decay, the atom loses 4 nucleons (protons and neutrons) because it emits an alpha particle.
[tex]\[
\text{Resulting Mass Number} = 209 - 4 = 205
\][/tex]
5. Identify the resulting element based on its atomic number:
The atomic number 81 corresponds to the element Thallium (Tl).
6. Compose the resulting atom:
The resulting atom is [tex]\({ }_{81}^{205} Tl\)[/tex].
7. Match the result with the given options:
A. [tex]\({ }_{81}^{205} TI\)[/tex] – This matches our result.
B. [tex]\({ }_{85}^{213} At\)[/tex] – Incorrect.
C. [tex]\({ }_{81}^{204} TI\)[/tex] – Incorrect mass number.
D. [tex]\({ }_{85}^{210} At\)[/tex] – Incorrect atomic and mass numbers.
The correct answer is A. [tex]\({ }_{81}^{205} TI\)[/tex]
