If a proton and anti-proton come close to each other and annihilate, how much energy will be released ?

Options

A. `1.5xx10^(-10)J`
B. `3xx10^(-10)J`
C. `4.5xx10^(-10)J`
D. None of these

Answer

To find the energy released when a proton and an anti-proton annihilate each other, we can follow these steps:

### Step 1: Determine the mass of the proton and anti-proton
The mass of a proton (m_p) and the mass of an anti-proton (m_a) are equal. Both have a mass of approximately:
\[ m_p = m_a = 1.67 \times 10^{-27} \text{ kg} \]

### Step 2: Calculate the total mass before annihilation
When a proton and an anti-proton come together, their total mass (m_total) before annihilation is:
\[ m_{total} = m_p + m_a = 1.67 \times 10^{-27} \text{ kg} + 1.67 \times 10^{-27} \text{ kg} = 2 \times 1.67 \times 10^{-27} \text{ kg} \]
\[ m_{total} = 3.34 \times 10^{-27} \text{ kg} \]

### Step 3: Use Einstein's mass-energy equivalence principle
According to Einstein's equation \( E = mc^2 \), the energy released (E) during the annihilation can be calculated using the total mass converted into energy:
\[ E = m_{total} \cdot c^2 \]
Where \( c \) (the speed of light) is approximately \( 3 \times 10^8 \text{ m/s} \).

### Step 4: Calculate the energy in joules
Substituting the values:
\[ E = (3.34 \times 10^{-27} \text{ kg}) \cdot (3 \times 10^8 \text{ m/s})^2 \]
\[ E = (3.34 \times 10^{-27}) \cdot (9 \times 10^{16}) \]
\[ E = 3.006 \times 10^{-10} \text{ joules} \]

### Step 5: Convert energy to mega electron volts (MeV)
We know that 1 MeV is equivalent to \( 1.6 \times 10^{-13} \text{ joules} \). To convert joules to MeV:
\[ E_{MeV} = \frac{E}{1.6 \times 10^{-13}} \]
\[ E_{MeV} = \frac{3.006 \times 10^{-10}}{1.6 \times 10^{-13}} \]
\[ E_{MeV} \approx 1.88 \times 10^{3} \text{ MeV} \]

### Step 6: Final energy released
Since we calculated the energy released in joules, we can conclude that the energy released during the annihilation of a proton and an anti-proton is approximately:
\[ E \approx 3.006 \times 10^{-10} \text{ joules} \]

### Conclusion
The energy released when a proton and an anti-proton annihilate each other is approximately \( 3.0 \times 10^{-10} \text{ joules} \).

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