STATEMENT-1 `:` The reaction, `""_(6) C^(11) rarr""_(5)B^(11)`, takes place with positron decay.
and
STATEMENT -2 `:` `( n)/( p ) ` ratio decreases in this change.

Options

A. STATEMENT-1 is True, STATEMENT-2 is True, STATEMENT-2 is correct explanation for STATEMENT-1
B. STATEMENT-1 is True, STATEMENT-2 is True, STATEMENT-2 is NOT a correct explanation for STATEMENT-1
C. STATEMENT-1 is True, STATEMENT-2 is False
D. STATEMENT-1 is False, STATEMENT-2 is True

Answer

To solve the problem, we need to analyze the two statements given:

**Statement 1:** The reaction \( _{6}^{11}C \rightarrow _{5}^{11}B \) takes place with positron decay.

**Statement 2:** The \( \frac{n}{p} \) ratio decreases in this change.

### Step-by-Step Solution:

1. **Understanding the Reaction:**
- The reaction shows the decay of Carbon-11 (\( _{6}^{11}C \)) into Boron-11 (\( _{5}^{11}B \)).
- In positron decay, a proton in the nucleus is converted into a neutron and a positron is emitted.

2. **Identifying the Particles:**
- For Carbon-11, the atomic number (Z) is 6, which means it has 6 protons.
- The mass number (A) is 11, so the number of neutrons (N) can be calculated as:
\[ N = A - Z = 11 - 6 = 5 \]
- Therefore, Carbon-11 has 6 protons and 5 neutrons.

3. **Decay Process:**
- In the decay \( _{6}^{11}C \rightarrow _{5}^{11}B \), one proton is transformed into a neutron.
- Thus, Boron-11 will have:
- Protons (Z) = 5
- Neutrons (N) = 11 - 5 = 6

4. **Calculating the \( \frac{n}{p} \) Ratio:**
- For Carbon-11:
\[ \frac{n}{p} = \frac{5}{6} \approx 0.833 \]
- For Boron-11:
\[ \frac{n}{p} = \frac{6}{5} = 1.2 \]

5. **Analyzing the \( \frac{n}{p} \) Ratio Change:**
- The ratio for Carbon-11 is approximately 0.833, and for Boron-11, it is 1.2.
- This indicates that the \( \frac{n}{p} \) ratio has **increased** from Carbon-11 to Boron-11.

6. **Conclusion:**
- **Statement 1** is true because the reaction does involve positron decay.
- **Statement 2** is false because the \( \frac{n}{p} \) ratio actually increases, not decreases.

### Final Answer:
- **Statement 1 is true.**
- **Statement 2 is false.**