A photon creates a pair of electron-positron with equal kinetic energy. Let kinetic energy of each particle is 0.29MeV. Then what should be energy of the photon

Options

A. 1.60 MeV
B. 1.63 MeV
C. 2.0 MeV
D. 1.90 MeV

Answer

To solve the question regarding the energy of the photon required to create a pair of electron-positron with equal kinetic energy, we can follow these steps:

### Step 1: Determine the minimum energy required for pair production
The minimum energy required to create an electron-positron pair is equal to the rest mass energy of the two particles. The rest mass energy of an electron (or positron) is given by:

\[ E = m c^2 \]

Where:
- \( m \) is the mass of the electron (approximately \( 9.11 \times 10^{-31} \) kg)
- \( c \) is the speed of light (\( 3 \times 10^8 \) m/s)

The rest mass energy of one electron is approximately \( 0.511 \) MeV. Therefore, for a pair (electron + positron), the minimum energy required is:

\[ E_{\text{min}} = 2 \times 0.511 \text{ MeV} = 1.022 \text{ MeV} \]

### Step 2: Calculate the total kinetic energy of the particles
Given that the kinetic energy of each particle (electron and positron) is \( 0.29 \text{ MeV} \), the total kinetic energy for both particles is:

\[ KE_{\text{total}} = 2 \times 0.29 \text{ MeV} = 0.58 \text{ MeV} \]

### Step 3: Calculate the total energy of the photon
The total energy of the photon must be the sum of the minimum energy required for pair production and the total kinetic energy of the particles:

\[ E_{\text{photon}} = E_{\text{min}} + KE_{\text{total}} \]

Substituting the values we calculated:

\[ E_{\text{photon}} = 1.022 \text{ MeV} + 0.58 \text{ MeV} = 1.602 \text{ MeV} \]

### Final Answer
The energy of the photon required to create the electron-positron pair with equal kinetic energy of \( 0.29 \text{ MeV} \) each is:

\[ E_{\text{photon}} = 1.602 \text{ MeV} \]

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