The Rest Energy of an Electron is the Rest Mass of the Electron (me) multiplied by the Square of the Velocity of Light or (9.11×10-31 Kilograms)(3×108 Meters Per Second)2 which gives 8.199×10-14 Joules. 1 Joule equals 1012 Picojoules, so 8.199×10-14 Joules × 1012 Picojoules Per Joule will give 0.08199 Picojoules (or 82 Thousandths of a Trillionth of a Joule).
The Kinetic Energy given to an Electron to accelerate it to 0.95c or 95% of the Velocity of Light is found by first determining Mass-Increase. Write m = (9.11×10-31 Kilograms) ÷ √[1 − (0.95c/c)2] or
[(9.11×10-31)/√(1 − 0.952)] Kilograms which reduces to 2.917534962×10-30 Kilograms.
Then compute ΔW or Kinetic Energy given as (m−me)c2 or
(2.917534962×10-30 − 9.11×10-31)(3×108)2 Kilogram-Dot-Meters-Squared Per Second Squared
(or kg•m2⁄s2), which simplifies to 1.805881466×10-13 Joules. 1.805881466×10-13 Joules × 1012 Picojoules Per Joule yields 0.1805881466 Picojoules.
Finally, write the Total Relativistic Energy sought as (0.08199 + 0.1805881466) or
0.2625781466 Picojoules.
