Positron is the antiparticle of an electron .It has the same mass as an electron but the opposite charge An electron and a positron moving towards each other with equal and opposite velocities.

Options

A. can annihilate into one photon. Conserving both energy and momentum
B. cannot annihilate into one photon because energy cannot be conserved
C. cannot annihilate into one photon because momentum cannot be conserved
D. cannot annihilate into one photon because charge cannot be conserved

Answer

### Step-by-Step Solution:

1. **Understanding the Concept of Annihilation**:
- When an electron (E-) and a positron (E+) collide, they can annihilate each other. This process is known as electron-positron annihilation. The result of this annihilation is the production of photons (light particles).

2. **Identifying the Properties of Electron and Positron**:
- An electron has a charge of -1 and a mass (m) of approximately 9.11 x 10^-31 kg.
- A positron has a charge of +1 and the same mass as the electron (9.11 x 10^-31 kg).

3. **Analyzing the Given Conditions**:
- The question presents four conditions regarding the annihilation of an electron and a positron into photons.
- We need to evaluate each condition based on the principles of conservation of energy, momentum, and charge.

4. **Condition 1: Can they annihilate into one quantum?**:
- Annihilation into one photon (quantum) is not possible because:
- **Energy Conservation**: The total energy before and after the annihilation must be equal. If they annihilate into one photon, the energy cannot be conserved as the photon would not have enough energy to account for both particles.
- **Momentum Conservation**: The initial momentum of the system (electron and positron) is non-zero (equal and opposite velocities). A single photon cannot carry this momentum, hence momentum would not be conserved.
- **Charge Conservation**: The total charge before annihilation is zero (−1 + 1 = 0), and a photon has no charge (0). Therefore, charge is conserved.

5. **Conclusion**:
- The electron and positron cannot annihilate into one photon because:
- Energy cannot be conserved.
- Momentum cannot be conserved.
- Charge is conserved.
- Therefore, the correct statement is that they cannot annihilate into one photon due to the conservation of momentum.

### Final Answer:
The electron and positron cannot annihilate into one photon because momentum cannot be conserved.

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