Which of the following statements is true ?

Options

A. `""_(78) Pt^(192)` has 78 neutrons
B. `""_(84) Po^(214) to ""_(82) Pb^(210) + beta^(-)`
C. `""_(92) U^(238) to ""_(90) Th^(234) + ""_(2) He^(4)`
D. `""_(90) Th^(234) to ""_(91) Pa^(234) + ""_(2) He^(4)`

Answer

To determine which statement is true among the given options, we will analyze each option based on the principles of nuclear physics, specifically focusing on the conservation of atomic number and mass number during nuclear reactions.

### Step-by-Step Solution:

1. **Understanding the Atomic Structure**:
- Each element has a specific atomic number (Z), which represents the number of protons in the nucleus, and an atomic mass number (A), which is the total number of protons and neutrons in the nucleus.

2. **Calculating Neutrons**:
- The number of neutrons (N) in a nucleus can be calculated using the formula:
\[ N = A - Z \]
- For Platinum (Pt), given that its atomic mass is 192 and atomic number is 78:
\[ N = 192 - 78 = 114 \]
- Since the option states 78, this is incorrect.

3. **Analyzing the First Reaction**:
- The first reaction involves a beta particle decay. A beta particle (β) is represented as \( \beta^- \) with a charge of -1.
- The equation provided is:
\[ \text{Reactants: } 84 \rightarrow 82 + \beta^- \]
- Balancing the atomic numbers:
- Left-hand side (LHS): 84
- Right-hand side (RHS): \( 82 - 1 = 81 \)
- Since LHS ≠ RHS, this statement is incorrect.

4. **Analyzing the Second Reaction**:
- The second reaction is:
\[ \text{Reactants: } 92 \rightarrow 90 + 2 \]
- Balancing the atomic numbers:
- LHS: 92
- RHS: \( 90 + 2 = 92 \)
- Balancing the mass numbers:
- LHS: 238
- RHS: \( 234 + 4 = 238 \)
- Both atomic number and mass number are balanced, so this statement is correct.

5. **Analyzing the Third Reaction**:
- The third reaction is:
\[ \text{Reactants: } 90 \rightarrow 91 + 2 \]
- Balancing the atomic numbers:
- LHS: 90
- RHS: \( 91 + 2 = 93 \)
- Since LHS ≠ RHS, this statement is incorrect.

### Conclusion:
The only true statement among the options is the second one, where both the atomic number and mass number are balanced.