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. `4.5 xx10^(-10)J`
D. `2xx10^(-10)J`

Answer

To solve the problem of how much energy is released when a proton and an anti-proton annihilate each other, we can follow these steps:

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

### Step 2: Calculate the Total Mass
When a proton and an anti-proton annihilate, the total mass (m_total) involved in the annihilation is:
\[ m_{total} = m_p + m_a = 1.67 \times 10^{-27} \text{ kg} + 1.67 \times 10^{-27} \text{ kg} = 2 \times 1.67 \times 10^{-27} \text{ kg} \]

### Step 3: Convert Mass to Energy
Using Einstein's mass-energy equivalence principle, \(E = mc^2\), we can calculate the energy released.

1. First, we convert the total mass into atomic mass units (amu):
\[ m_{total} = 2 \text{ amu} \]

2. The energy equivalent of 1 amu is given as:
\[ E_{1 \text{ amu}} = 931.5 \text{ MeV} \]

3. Therefore, the energy released (E) for 2 amu is:
\[ E = 2 \times 931.5 \text{ MeV} = 1863 \text{ MeV} \]

### Step 4: Convert MeV to Joules
To convert MeV to Joules, we use the conversion factor:
\[ 1 \text{ MeV} = 1.6 \times 10^{-13} \text{ Joules} \]

Thus, the energy in Joules is:
\[ E = 1863 \text{ MeV} \times 1.6 \times 10^{-13} \text{ Joules/MeV} \]

### Step 5: Calculate the Final Energy in Joules
Now we perform the multiplication:
\[ E = 1863 \times 1.6 \times 10^{-13} \text{ Joules} \]
\[ E \approx 2.9808 \times 10^{-10} \text{ Joules} \]

### Step 6: Approximate the Result
Rounding this value gives:
\[ E \approx 3 \times 10^{-10} \text{ Joules} \]

### Conclusion
The energy released when a proton and an anti-proton annihilate each other is approximately:
\[ \boxed{3 \times 10^{-10} \text{ Joules}} \]