A `1 MeV` positron encounters a `1 MeV` electron travelling in opposite direction. The total energy released is (In `MeV`)

Options

A. `2`
B. `3.02`
C. `1.02`
D. `2.04`

Explanation

To solve the problem of finding the total energy released when a 1 MeV positron encounters a 1 MeV electron traveling in opposite directions, we can follow these steps:

### Step 1: Understand the Initial Energy
The total initial energy of the system consists of the rest mass energy and kinetic energy of both the positron and the electron.

- The rest mass energy of both the positron and the electron is approximately 0.51 MeV each.
- The kinetic energy of the positron is 1 MeV, and the kinetic energy of the electron is also 1 MeV.

### Step 2: Calculate the Total Initial Energy
The total initial energy (E_initial) can be calculated as follows:

\[ E_{\text{initial}} = (\text{Rest mass energy of positron}) + (\text{Rest mass energy of electron}) + (\text{Kinetic energy of positron}) + (\text{Kinetic energy of electron}) \]

Substituting the values:

\[ E_{\text{initial}} = 0.51 \, \text{MeV} + 0.51 \, \text{MeV} + 1 \, \text{MeV} + 1 \, \text{MeV} \]

\[ E_{\text{initial}} = 0.51 + 0.51 + 1 + 1 = 3.02 \, \text{MeV} \]

### Step 3: Understand the Final Energy
In the annihilation process, the positron and electron annihilate each other, resulting in the production of gamma rays (photons). The total energy of the photons produced is equal to the initial energy of the positron and electron before annihilation.

The final energy (E_final) after annihilation is:

\[ E_{\text{final}} = 0 \, \text{MeV} \quad (\text{since photons have no rest mass}) \]

### Step 4: Calculate the Energy Released
The energy released during the annihilation can be calculated using the formula:

\[ \text{Energy released} = E_{\text{initial}} - E_{\text{final}} \]

Substituting the values:

\[ \text{Energy released} = 3.02 \, \text{MeV} - 0 \, \text{MeV} = 3.02 \, \text{MeV} \]

### Conclusion
The total energy released during the annihilation of the positron and electron is **3.02 MeV**.

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