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Question

If a proton and anti-proton come close to each other and annihilate, how much energy will be released?


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Solution

Step 1: Calculating the total mass :-

An antiproton is defined as a nucleon with the same mass but the opposite charge to that of a proton. Because of this, when a proton and an antiproton collide, their combined masses are twice as large as a proton.
m=2×mp

where m is combined mass

mp is mass of proton

Mass of proton in (amu) mp=1amu=1.67×10-27kg

So, m=2mp=2×1.67×10-27kg=3.34×10-27kg

Step 2: Conversion of mass into energy :-

When the proton and antiproton combine, the combined particles annihilate by transforming all of their mass into energy:

According to Einstein's mass-energy equivalence theory,E=mc2

where m is mass

c=3×108ms-1, is speed of light

Therefore,

E=3.34×10-27kg×(3×108ms-1)2E=3.34×10-27×9×1016JE=30.06×10-27+16JE=30.06×10-11JE=3.006×10-10J3×10-10J

So, Energy released will be 3×10-10J.


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