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

\[= \frac{2 \times 9 . 1 \times 9 \times {10}^{- 15}}{1 . 6 \times {10}^{- 19}}\]
\[ = 102 . 37 \times {10}^4 eV\]
\[ = 1 . 02 \times {10}^5 eV\]
\[ = 1 . 02 MeV\]