What is one half the speed of light?

Answer 1

The characteristic wavelength of an electron = h / p, where

h = Planck's constant;

p = the electron linear momentum = electron mass * speed = g * electron rest mass * speed; and

g = the Lorentz factor to account for the electron-mass change with speed.

Known facts:

h = 6.63 × 10-34 [J s]

electron rest mass, me = 9.11×10-31 [kg]

electron speed, v = 1.5x108 [m/s]

c = speed of light in vacuum = 3x108 [m/s]

v/c = 0.5

g = 1/sqrt(1 - v2/c2) = 1/sqrt(0.75) = 1.1547

Therefore, p = 1.1547 * 9.11×10-31 [kg] * 1.5x108 [m/s] = 2.7e-29 [kg m s-1]

Hence, the electron wavelength

= 6.63 × 10-34 [J s] / 2.7e-29 [kg m s-1]

= 2.46e-5 [m] or 2.46x10-5 [m].

Q.E.D.

=========================

Answer 2

c/2 = 149,896,229 meters (93,141.2 miles) per second, in vacuum.

In material media, divide this number by the refractive index of the medium

to find one half of the speed of light in that medium.