Final answer:
When a positron and an electron collide, they annihilate and convert their mass into energy as per E = mc², releasing 1.64 × 10⁻¹³ joules of energy in the form of gamma rays. The resultant energy can then be used to calculate the velocity imparted to a proton or another electron as kinetic energy.
Step-by-step explanation:
When a positron, the antimatter counterpart of the electron, comes in contact with an electron, they undergo a process known as annihilation. This reaction converts the entirety of their mass into energy, as described by Albert Einstein's famous equation E = mc². Given that the mass of an electron (and thus a positron) is 9.11 × 10⁻³¹ kg, the energy released from such annihilation can be calculated by doubling this mass (to account for both the electron and the positron) and then multiplying by the square of the speed of light (c²).
The calculation yields Eo = 2(9.11 × 10⁻³¹ kg) (3.00 × 10⁸ m) ² = 1.64 × 10⁻¹³ J, signifying how much energy is released in the form of gamma rays during annihilation. When this energy is given to a proton as kinetic energy, the resulting velocity can be found using the kinetic energy formula ½mv² = E, where 'm' is the mass of the proton and 'v' is its velocity. Similarly, for another electron receiving the same amount of kinetic energy, the velocity would be much higher due to the substantially lower mass of the electron compared to the proton.