What is the minimum energy required to produce an electron-positron pair?

[arpon]

Homework Statement

The antiparticle of electron is positron, whose mass is the same as electrons, i.e. $9.1 * 10^{-31} kg$ but the charge is opposite. What is the minimum energy required to produce a electron-positron pair?

2. Homework Equations
$E = mc^2$

The Attempt at a Solution

Actually I thought, it would be just $E = mc^2$. But the answer doesn't match.

 

[ShayanJ]

You should calculate the energy required to produce a pair of particles i.e. two particles with equal masses!

 

[arpon]

$2*mc^2$ ?

 

[ShayanJ]

Yeah!

 

[HalfLostAndSearching]

The minimum energy required to produce an electron-positron pair is actually given by the formula E = 2mc^2, where m is the mass of either the electron or the positron. This is because the energy needed to create a pair of particles is equal to the total energy of both particles, which in this case is twice the energy of a single particle. So the minimum energy required would be 2 * 9.1 * 10^-31 kg * (3*10^8 m/s)^2 = 1.64 * 10^-13 J.