A positron is an antimatter version of the electron, having exactly the same mass. When a positron and an electron meet. they annihilate, converting all of their mass into energy. (a) Fund the energy released, assuming negligible kinetic energybefore the annihilation. (b) If this energy is given to a proton in the form of kinetic energy, what is its velocity"? (c) If thisenergy is given to another electron in the form of kinetic energy. what is its velocity?

Energy equivalent of mass m is given by Einstein''s mass energy formula

E = mc², m is mass and c is speed of light.

mass of electron = mass of positron

= 9.1 x 10⁻³¹ kg

Total mass = 2 x 9.1 x 10⁻³¹ kg

Energy equivalent = mc²

= 2 x 9.1 x 10⁻³¹ x (3 x 10⁸) ²

= 163.8 x 10⁻¹⁵ J

b) Let v be the velocity of proton when this energy is given to it. Mass of proton is 1.67 x 10⁻²⁷ kg

So equating the two energy

1/2 x 1.67 x 10⁻²⁷ x v² = 163.8 x 10⁻¹⁵

v² = 196 x 10¹²

v = 14 x 10⁶ m / s

c) If this energy is given to a single electron and v is its velocity

1/2 m v² = 163.8 x 10⁻¹⁵

.5 x 9.1 x 10⁻³¹ v² = 163.8 x 10⁻¹⁵

v² = 36 x 10¹²

v = 6 x 10⁶ m/s