Sure, let's go through the process of understanding the beta decay of Phosphorus-32 step-by-step.
1. Understand Beta Decay:
- Beta decay is a type of radioactive decay where a beta particle (which is an electron or a positron) is emitted.
- In beta-minus decay, a neutron in the nucleus transforms into a proton, emitting an electron ([tex]${ }_{-1}^0 e$[/tex]) and an anti-neutrino.
2. Write the Initial Nucleus:
- The element Phosphorus-32 is represented as [tex]${ }_{15}^{32} P$[/tex].
3. Identify the Resulting Nucleus After Beta-Minus Decay:
- When Phosphorus-32 undergoes beta-minus decay, a neutron is converted into a proton. This increases the atomic number by 1 but leaves the mass number unchanged.
- Therefore, the resulting element after this process will have an atomic number of 16, and it will be Sulfur-32, represented as [tex]${ }_{16}^{32} S$[/tex].
4. Balance the Equation:
- The equation for beta-minus decay can be written as:
[tex]\[
{ }_{15}^{32} P \rightarrow{ }_{16}^{32} S + \text{ ? }
\][/tex]
- To balance both the atomic number and the mass number, we need to add the beta particle, which is an electron represented as [tex]${ }_{-1}^0 e$[/tex].
- The atomic number on the left side is 15, and on the right side, it is [tex]\(16 - 1 = 15\)[/tex].
- The mass number on both sides is 32, ensuring that they are equal.
5. Identify the Correct Choice:
- The particle that correctly completes the equation is [tex]${ }_{-1}^0 e$[/tex].
Therefore, the correct answer is:
A. [tex]${ }_{-1}^0 e$[/tex].
