When and electron-positron pair annihilates, the energy released is about.

Options

A. a.`0.8xx10^(-13)J`
B. b.`1.6xx10^(-13)J`
C. c.`3.2xx10^(10-13)J`
D. d.`4.8xx10^(-13)J`

Explanation

To solve the problem of determining the energy released when an electron-positron pair annihilates, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Annihilation Process**:
When an electron (e⁻) and a positron (e⁺) collide, they annihilate each other, resulting in the production of gamma rays. The energy released during this process is equivalent to the total rest mass energy of the electron and positron.

2. **Identify the Rest Mass Energy**:
The rest mass energy (E) of an electron (or positron) can be calculated using the formula:
\[ E = m c^2 \]
where \( m \) is the rest mass of the particle and \( c \) is the speed of light. The rest mass energy of an electron (and positron) is approximately 0.511 MeV (mega electron volts).

3. **Calculate Total Energy**:
Since both the electron and positron have the same rest mass energy, the total energy released during their annihilation can be calculated as:
\[ \text{Total Energy} = 2 \times 0.511 \text{ MeV} = 1.022 \text{ MeV} \]

4. **Convert MeV to Joules**:
To convert the energy from MeV to Joules, we use the conversion factor:
\[ 1 \text{ MeV} = 1.6 \times 10^{-13} \text{ Joules} \]
Therefore, we can convert the total energy:
\[ 1.022 \text{ MeV} = 1.022 \times 1.6 \times 10^{-13} \text{ Joules} \]
\[ = 1.6352 \times 10^{-13} \text{ Joules} \]

5. **Final Result**:
The energy released when an electron-positron pair annihilates is approximately \( 1.6352 \times 10^{-13} \) Joules.