Determine the Energy of Electromagnetic Radiation After Particle Collision

[tobywashere]

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:

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.

 

[hadoque]

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...

 

[tobywashere]

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