Alpha decay of `._(92)^(238)U` forms `._(90)^(234)Th`. What kind of decay from `._(90)^(234)Th` produces `._(84)^(234)Ac` ?

Options

A. `alpha`
B. `beta`
C. `beta^(+)`(positron)
D. `gamma` -emission

Answer

To solve the problem, we need to analyze the decay process of Thorium-234 (Th-234) to determine what type of decay produces Actinium-234 (Ac-234).

### Step-by-Step Solution:

1. **Identify the Initial and Final Nuclides**:
- The initial nuclide is Thorium-234, represented as \( _{90}^{234}Th \).
- The final nuclide is Actinium-234, represented as \( _{84}^{234}Ac \).

2. **Determine the Change in Atomic Number**:
- The atomic number of Thorium (Th) is 90.
- The atomic number of Actinium (Ac) is 89.
- The change in atomic number is \( 90 - 89 = 1 \). This indicates that the atomic number decreases by 1.

3. **Determine the Change in Mass Number**:
- The mass number of both Thorium-234 and Actinium-234 is 234.
- The change in mass number is \( 234 - 234 = 0 \). This indicates that the mass number remains unchanged.

4. **Identify the Type of Decay**:
- Since the atomic number decreases by 1 and the mass number remains unchanged, this type of decay corresponds to either positron emission or electron capture.
- In positron emission (beta plus decay), a proton is converted into a neutron, resulting in a decrease in atomic number by 1 while keeping the mass number the same.
- In electron capture, an electron is captured by the nucleus, which also results in a decrease in atomic number by 1 with no change in mass number.

5. **Conclusion**:
- Both positron emission and electron capture could lead to the formation of Actinium-234 from Thorium-234. However, since the question specifies a type of decay, we can conclude that the decay from Thorium-234 to Actinium-234 is best described as **positron emission**.

### Final Answer:
The type of decay from \( _{90}^{234}Th \) that produces \( _{84}^{234}Ac \) is **positron emission**.

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