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

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As we know electron and proton has same mass i.e.

As they annihilate and produces gamma particle with some energy

There is a physical significance of special theory of relativity that Energy and mass are interchangeable and that is given by Sir Einstein famous equation .

Answer 2

Explanation:

It is known that,

Electron Mass = Positron Mass = $9.1 \times 10^{-31} \mathrm{kg}$

Both the positron and the electron are charged oppositely and thrash each other in order to form a mass zero gamma photon of rest. So,

$\text { â'tm }=m_{p}+m_{e}=2 \times 9.1 \times 10^{-31} \mathrm{kg}$

This mass will be transformed into the resulting γ photon’s energy. So,

$E_{y}=\hat{\mathbf{a}}^{\prime}+m c^{2}$

$E_{\mathrm{y}}=2 \times 10^{-31} \times 9.1 \times 9 \times 10^{16} \mathrm{J}$

$=102.37 \times 104 \mathrm{eV}=1.02 \mathrm{MeV}$