A gamma ray photon creates an electron-positron pair. If the rest mass energy of an electron is `0.5 MeV` and the total `K.E.` of the electron-position pair is `0.78 MeV`, then the energy of the gamma ray photon must be.

Options

A. 0.78 MeV
B. 1.78 MeV
C. 1.28 MeV
D. 0.28 MeV

Explanation

To find the energy of the gamma ray photon that creates an electron-positron pair, we can follow these steps:

### Step 1: Understand the energy contributions
The energy of the gamma ray photon is used to create an electron-positron pair. The total energy of the photon must account for both the rest mass energy of the particles created and their kinetic energy.

### Step 2: Calculate the rest mass energy of the pair
The rest mass energy of an electron is given as \(0.5 \, \text{MeV}\). Since the positron has the same rest mass as the electron, the rest mass energy of the positron is also \(0.5 \, \text{MeV}\).

Thus, the total rest mass energy of the electron-positron pair is:
\[ \text{Total Rest Mass Energy} = \text{Rest Mass Energy of Electron} + \text{Rest Mass Energy of Positron} = 0.5 \, \text{MeV} + 0.5 \, \text{MeV} = 1.0 \, \text{MeV} \]

### Step 3: Add the kinetic energy
The total kinetic energy of the electron-positron pair is given as \(0.78 \, \text{MeV}\).

### Step 4: Calculate the total energy of the photon
Now, we can find the total energy of the gamma ray photon by adding the total rest mass energy and the total kinetic energy:
\[ \text{Total Energy of Photon} = \text{Total Rest Mass Energy} + \text{Total Kinetic Energy} = 1.0 \, \text{MeV} + 0.78 \, \text{MeV} = 1.78 \, \text{MeV} \]

### Conclusion
Thus, the energy of the gamma ray photon must be \(1.78 \, \text{MeV}\).

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