To determine the particle that completes the nuclear equation, we need to analyze the changes in atomic number and mass number between the reactant and the product.
Given the nuclear equation:
[tex]\[{}^{124}_{56} \text{Ba} \rightarrow {}^{124}_{55} \text{Cs} + \text{?}\][/tex]
First, let's identify the properties of the given elements:
1. Barium ([tex]\( {}^{124}_{56} \text{Ba} \)[/tex]):
- Atomic number (protons) = 56
- Mass number = 124
2. Cesium ([tex]\( {}^{124}_{55} \text{Cs} \)[/tex]):
- Atomic number (protons) = 55
- Mass number = 124
The goal is to determine the missing particle that balances this nuclear equation. To do this, we need to compare the atomic numbers and mass numbers before and after the reaction.
1. Change in atomic number (protons):
- Initial atomic number (Barium) = 56
- Final atomic number (Cesium) = 55
- The change in atomic number = 56 - 55 = 1
Since the atomic number decreases by 1, it indicates that 1 proton has been converted into a different particle.
2. Change in mass number:
- Initial mass number (Barium) = 124
- Final mass number (Cesium) = 124
- The change in mass number = 124 - 124 = 0
The mass number remains the same, meaning there is no change in the total number of nucleons (protons and neutrons).
Considering the decrease in atomic number without a change in mass number, the missing particle is likely an electron ([tex]\( e \)[/tex]) emitted during the process. This kind of reaction is known as beta-minus (β⁻) decay, where a neutron is converted into a proton, and an electron (beta particle) is emitted.
Thus, the emitted particle can be represented as:
[tex]\[ {}^0_{-1} e \][/tex]
So, the complete nuclear equation is:
[tex]\[{}^{124}_{56} \text{Ba} \rightarrow {}^{124}_{55} \text{Cs} + {}^0_{-1} e\][/tex]
Hence, the particle that completes the nuclear equation is:
[tex]\[{}^0_{-1} e\][/tex]
Therefore, the correct option is:
[tex]\[{}^0_{-1} e\][/tex]
