Where do electrons get the energy to travel at such high speeds?
Asked by: Matthew Lammens
Answer
Electrons are charged particles. That is, they carry an electric charge. For this reason, they are influenced by electric fields. More precisely, they are accelerated in an electric field.
Since the mass of an electron is so very small compared with objects of ordinary experience, electrons are accelerated to very high velocities even by electric fields of only a few volts [per meter].
For example, the electrons in orbit in an atom have been accelerated through an electric field of only a few volts created by the positively charged nucleus as they 'fall' into the atom and are captured in orbit. Just these few volts are enough, due to the extremely small mass of the electron [mass of the electron is = 9.10938 x 10^{-31} kg], to result in the electron attaining orbital speeds that, in some cases, may be an appreciable fraction of the speed of light.
Put another way, the fact that electrons usually seem to travel at very high speeds is not, as one might otherwise think, an indication of great energy.
It is because the mass of the electron is so small that its speed will be very great even when the electron has absorbed only a very small amount of energy.
To be more precise, for a non-relativistic particle, the speed v is given by
v = sqrt(2E/m)
, where E is the kinetic energy and m the mass of the particle. As you can see, if m is very small, v may be very large for a modest energy E.
Answered by: Warren Davis, Ph.D., President, Davis Associates, Inc., Newton, MA USA
'Physics is mathematical not because we know so much about the physical world, but because we know so little; it is only its mathematical properties that we can discover.'