The number of `alpha beta -`particles emitted in the nucleus reaction `._(92)U^(238) rarr ._(90)Th^(234) rarr ._(91)Pa^(234)` are respectively

Options

A. 1 and 1
B. 1 and 2
C. 2 and 1
D. 2 and 2

Explanation

To solve the problem of determining the number of alpha and beta particles emitted in the nuclear reactions given, we can break it down step by step.

### Step-by-Step Solution:

1. **Identify the Initial Reaction**:
The first part of the reaction is:
\[ _{92}^{238}U \rightarrow _{90}^{234}Th \]
Here, Uranium-238 (U-238) is transforming into Thorium-234 (Th-234).

2. **Analyze the Change in Mass and Atomic Number**:
- The atomic number of Uranium (92) decreases to Thorium (90). This indicates a loss of 2 in the atomic number.
- The mass number decreases from 238 to 234, which indicates a loss of 4 in the mass number.

3. **Determine the Type of Particle Emitted**:
The emission of an alpha particle (α) results in a decrease of 2 in the atomic number and a decrease of 4 in the mass number. Thus, since both the atomic number and mass number have changed as calculated:
- **Alpha particles emitted**: 1 (since 2 units of charge and 4 units of mass are lost).

4. **Identify the Second Reaction**:
The second part of the reaction is:
\[ _{90}^{234}Th \rightarrow _{91}^{234}Pa \]
Here, Thorium-234 (Th-234) is transforming into Protactinium-234 (Pa-234).

5. **Analyze the Change in Mass and Atomic Number**:
- The atomic number increases from 90 to 91, indicating a gain of 1 in the atomic number.
- The mass number remains the same (234), indicating no change in mass.

6. **Determine the Type of Particle Emitted**:
The emission of a beta particle (β) results in an increase of 1 in the atomic number while keeping the mass number unchanged. Thus, since the atomic number has increased by 1:
- **Beta particles emitted**: 1 (since 1 unit of charge is gained).

### Final Answer:
- **Number of Alpha particles emitted**: 1
- **Number of Beta particles emitted**: 1

### Summary:
The number of alpha and beta particles emitted in the nuclear reactions is:
- Alpha particles: 1
- Beta particles: 1

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