Question

An electron and a positron moving at small speeds collide and annihilate each other. Find the energy of the resulting gamma photon.

Answer 1

We know,
Mass of electron = Mass of positron = 9.1 × 10⁻³¹ kg

Both are oppositely charged and annihilate each other to form a gamma photon of rest mass zero. Thus,
∆m = m_e + m_p = 2 × 9.1 × 10⁻³¹ kg

This mass will be converted into energy of the resulting γ photon. Thus,
E_γ= ∆mc²
E_{γ =} 2 × 9.1 × 10⁻³¹ × 9 × 10¹⁶ J
$$\begin{gathered} =\frac{2\times 9.1\times 9\times {10}^{-15}}{1.6\times {10}^{-19}} \\ =102.37\times {10}^4\mathrm{eV} \\ =1.02\times {10}^5\mathrm{eV} \\ =1.02\mathrm{MeV} \end{gathered}$$