Determine the Energy of Electromagnetic Radiation After Particle Collision

AI Thread Summary
In a collision between an electron and a positron, both with a rest mass of 9.11 x 10-31 kg and moving at 0.20c, the total energy calculated was 1.67 x 10-13 J, which is converted into electromagnetic radiation after the particles vanish. The initial calculation was based on the total energy formula, but a mistake was identified regarding the squaring of the speed of light, c. The textbook's answer of 0.615 MeV (9.84 x 10-14 J) was questioned, suggesting possible errors in both the calculations and the textbook. After correcting the calculation error, the final energy of the electromagnetic radiation remains at 1.67 x 10-13 J. This highlights the importance of careful calculations in physics problems.
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Homework Statement


The positron and the electron each have a rest mass of 9.11 x 10-31 kg. In a certain experiment, an electron and a positron collide and vanish, leaving only electromagnetic radiation after the interaction. Each particle is moving at a speed of 0.20c relative to the laboratory before the collision. Determine the energy of the electromagnetic radiation.

Homework Equations


Total energy of a particle:

sqrt-1-v2-c2-mc2-over-e.png


The Attempt at a Solution



Using the equation:

(9.11 x 10-31)c2 / sqrt[1 - (0.2c)2/c2]
= 8.37 x 10-14 J
This is the total energy of one electron or positron. Since two particles are colliding, the total energy of the system is 8.37x10-14 x 2 = 1.67 x 10-13 J
When the particles vanish, all the energy is converted to electromagnetic radiation, so the energy of the electromagnetic radiation is 1.67 x 10-13 J
However, the answer in my textbook says 0.615 MeV, which is 9.84 x 10-14 J. My textbook is known to have mistakes, so I am checking if this is my mistake or the textbook's mistake.
 
Last edited:
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Ok, a quick check. The energy must be E>mc^2. Mass is m = 2*9.1e-31kg, c = 3e8m/s, so E > 1.6e-13J
So it's possible both you and your book is wrong...
 


Sorry, I made a calculation error. I forgot to square c.
I edited my previous post. Now my answer is 1.67 x 10-13 J
 
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