Question

002 10.0 points note: report your answer in joules here. a proton and an antiproton, both at rest with respect to one another, mutually annihilate into two gamma rays. how much energy is produced in this annihilation? answer in units of j.

Answer 1

The mass of the proton is:
$m_p = 1.67 \cdot 10^{-27} kg$
and the mass of the antiproton is exactly the same, so the total mass of the two particles is $2m_p$.

In the annihilation, all the mass of the two particles is converted into energy, and the amount of this energy is given by Einstein's equivalence between mass and energy:
$E=Mc^2$
where M is the mass converted into energy and c is the speed of light. In this example, $M=2m_p$, therefore the energy released is
$E=2m_p c^2 = 2 (1.67 \cdot 10^{-27} kg)(3\cdot 10^8 m/s)^2=3 \cdot 10^{-10}J$