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A positron and an electron, each with a rest mass of 9.11 x 10^-31 kg, collide and completely annihilate into gamma rays. Using c = 3.00 x 10^8 m/s, what is the total energy of the gamma rays produced?
A8.19 x 10^-14 J
B1.64 x 10^-13 J
C3.28 x 10^-13 J
D1.64 x 10^-10 J
Answer & Solution
Correct answer: B. 1.64 x 10^-13 J
1. Each particle's rest energy is mc^2, and since both masses vanish, the total energy is 2mc^2.
2. Substitute m = 9.11 x 10^-31 kg and c = 3.00 x 10^8 m/s.
3. Compute mc^2 for one particle: (9.11 x 10^-31)(3.00 x 10^8)^2 = 8.199 x 10^-14 J.
4. Double this for both particles: 2 x 8.199 x 10^-14 = 1.64 x 10^-13 J.
5. 8.19 x 10^-14 J forgets to double for the second particle, and 3.28 x 10^-13 J doubles it twice.
6. 1.64 x 10^-10 J shifts the decimal point three places too far.
7. So 1.64 x 10^-13 J is correct.
_Source: OpenStax Physics (CC BY 4.0), Ch 10 "Special Relativity", section 10.2 Consequences of Special Relativity_
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