Question

The mass of an electron is me = 9.109x10^−31 kg, and the speed of light is c = 3x10^8 m/s.
Its rest energy mec2 = 8.2x10^−14 J, or mec2 = 0.51x10^6 eV, where 1 eV=1.6x10^−19 J. If
relativity were not true, find what accelerating voltage Vacc would be enough to accelerate
the electron starting from rest to a final speed equal to the speed of light, that is vfinal = c.

Answer 1

The mass of an electron is m_e = 9.109x10⁻³¹ kg

speed of light is c = 3x10⁸ m/s

rest energy mec2 = 8.2x10^−14 J

accelerating voltage Vacc = ?

But energy of an electron accelarating at potential Vacc is equal to rest mass energy and is given by

qVacc = m_ec² , where q = charge of electron = 1.6x10^−19

1.6x10^−19xVacc = 8.2x10^−14

Vacc = 8.2x10^−14 / 1.6x10^−19 = 0.51x10^6 V

Vacc = 0.51x10^6 V is enough to accelerate the electron starting from rest to a final speed equal to the speed of light