- Analyze the provided nuclear equation \({}_{6}^{14} \text{C} \rightarrow {}_{7}^{14} \text{N} + {}_{-1}^{0} e\), noting the change from atomic number 6 to 7 and the emission of an electron.
- Compare these characteristics against standard radioactive decay types: alpha, gamma, beta-plus, and beta-minus.
- Observe that the increase in atomic number and the emission of an electron are the defining features of beta-minus decay.
- Conclude that the equation models \(\boxed{\text{beta-minus decay}}\).
Explanation
- Analyzing the Nuclear Equation
The given nuclear equation is \({}_{6}^{14} \text{C} \rightarrow {}_{7}^{14} \text{N} + {}_{-1}^{0} e\).
To identify the type of decay, we examine the changes in the atomic number and the mass number of the nucleus, as well as the identity of the emitted particle.
- The initial nucleus is Carbon-14 (\({}_{6}^{14} \text{C}\)), which has an atomic number \(Z = 6\) and a mass number \(A = 14\).
- The final nucleus is Nitrogen-14 (\({}_{7}^{14} \text{N}\)), which has an atomic number \(Z = 7\) and a mass number \(A = 14\).
- The emitted particle is \({}_{-1}^{0} e\), which represents an electron (a beta-minus particle).
- Identifying the Decay Type
We compare the given reaction with the characteristics of different types of radioactive decay:
- Alpha decay: The nucleus emits an alpha particle (\({}_{2}^{4} \text{He}\)). The atomic number decreases by 2 and the mass number decreases by 4.
- Gamma decay: The nucleus emits a high-energy photon (\({}_{0}^{0} \gamma\)). Neither the atomic number nor the mass number changes.
- Beta-minus decay (\(\beta^-\)): A neutron in the nucleus converts into a proton and an electron. The electron (\({}_{-1}^{0} e\)) is emitted. As a result, the atomic number increases by 1, while the mass number remains unchanged.
- Beta-plus decay (\(\beta^+\)): A proton in the nucleus converts into a neutron and a positron. The positron (\({}_{+1}^{0} e\)) is emitted. As a result, the atomic number decreases by 1, while the mass number remains unchanged.
In our equation, the atomic number increases from 6 to 7, and an electron (\({}_{-1}^{0} e\)) is emitted. This matches the description of beta-minus decay perfectly.
- Conclusion
Based on the analysis, the reaction \({}_{6}^{14} \text{C} \rightarrow {}_{7}^{14} \text{N} + {}_{-1}^{0} e\) represents the transformation of a neutron into a proton within the Carbon-14 nucleus, accompanied by the emission of an electron. This is the definition of beta-minus decay. Thus, the equation models beta-minus decay. The final answer is \(\boxed{\text{beta-minus decay}}\).
Examples
Radioactive decay is not just a theoretical concept; it has practical applications in fields like archaeology. Carbon-14 dating relies on the beta-minus decay of Carbon-14 isotopes found in organic materials. By measuring the ratio of the remaining Carbon-14 to the stable Nitrogen-14, scientists can determine the age of ancient artifacts, such as fossils or wooden structures, providing a window into the past. Understanding these decay processes helps us date objects that are thousands of years old with remarkable precision.