Question

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) Find the energy released, assuming negligible kinetic energy before the annihilation.

a) 1.022 MeV
b) 0.511c
c) 0.511c
d) 1.022c

Answer 1

The energy released during the annihilation of an electron-positron pair is found using the equation E = mc² and is equal to 1.022 MeV. Option (a) 1.022 MeV is the correct answer.

Step-by-step explanation:

The question deals with the annihilation of a positron and an electron, during which their mass is converted entirely into energy. According to Einstein's famous equation E = mc², the energy (E) released can be calculated by multiplying the mass (m) of both the electron and positron by the speed of light squared (c²).

The rest mass of an electron (and positron) is approximately 9.11 × 10⁻³¹ kg, and the speed of light (c) is 3.00 × 10⁸ m/s. Therefore, the energy released during the annihilation of an electron-positron pair is:

E = 2(m)(c²) = 2(9.11 × 10⁻³¹ kg)(3.00 × 10⁸ m/s)² = 1.64 × 10⁻¹³ joules

Converting this energy to megaelectronvolts (MeV), we use the conversion factor 1 joule = 6.242 × 10¹¸ MeV:

E = 1.64 × 10⁻¹³ J × 6.242 × 10¹¸ MeV/J = 1.022 MeV. Therefore, the correct option is (a) 1.022 MeV.