Consider the following nuclear reactions and select the correct statemetns from the option given below .
Reaction I `n to p+e^(-)+v` Reaction II: `pton+e^(+)+v`

Options

A. Free neutron is unstable, therefore reaction I is possible
B. Free proton is stable, therefore reactionII is not possible
C. Inside a nucleus, both decays (reactions I and II) are possible
D. Inside a nucleus, reaction I is not possible but reaction II is possible.

Answer

To analyze the given nuclear reactions and determine the correct statements, let's break down the reactions and their implications step by step.

### Step 1: Understand the Reactions
1. **Reaction I**: \( n \rightarrow p + e^{-} + \nu \)
- This reaction shows a neutron (\( n \)) decaying into a proton (\( p \)), an electron (\( e^{-} \)), and a neutrino (\( \nu \)). This is known as beta decay (specifically beta minus decay).

2. **Reaction II**: \( p \rightarrow n + e^{+} + \nu \)
- This reaction depicts a proton (\( p \)) decaying into a neutron (\( n \)), a positron (\( e^{+} \)), and a neutrino (\( \nu \)). This is known as beta plus decay.

### Step 2: Analyze Stability of Neutrons and Protons
- **Free Neutrons**: Neutrons are unstable when they are in a free state (not bound within a nucleus). They have a half-life of about 14 minutes before they decay into protons, electrons, and neutrinos.
- **Free Protons**: Protons are stable in a free state. They do not decay under normal conditions.

### Step 3: Evaluate the Reactions
- **Reaction I**: Since free neutrons are unstable, this reaction is possible. Neutrons can decay into protons, electrons, and neutrinos when they are not bound in a nucleus.
- **Reaction II**: Free protons are stable and do not decay. Therefore, this reaction cannot occur in a free state.

### Step 4: Consider the Reactions Inside a Nucleus
- Inside a nucleus, both types of decay can occur:
- Neutrons can decay into protons (Reaction I).
- Protons can also convert into neutrons under certain conditions (Reaction II), such as in the presence of high-energy environments or during certain types of nuclear reactions.

### Step 5: Summarize the Findings
1. **Statement A**: Free neutrons are unstable - **True** (Reaction I is possible).
2. **Statement B**: Free protons are stable - **True** (Reaction II is not possible).
3. **Statement C**: Inside a nucleus, both decays are possible - **True**.
4. **Statement D**: Inside a nucleus, Reaction I is not possible - **False** (Reaction I is indeed possible inside a nucleus).

### Conclusion
The correct statements regarding the nuclear reactions are:
- A: True
- B: True
- C: True
- D: False