A decade before Einstein published his theory of relativity, J. J. Thomson propo

Question

A decade before Einstein published his theory of relativity, J. J. Thomson proposed that the electron might consist of small parts and attributed the electron's mass m to the electric potential energy of the interaction of the parts. Furthermore, he suggested that the energy equals mc2, where c is the speed of light. Make a rough estimate of the electron mass in the following way: Assume the electron is composed of three identical parts that are brought in from infinity and placed at the vertices of an equilateral triangle having sides equal to the classical radius of the electron, 2.82 x 10-15 m. (a) Find the total electric potential energy of this arrangement. (b) Divide by c2 to get an estimate of the electron mass. (c) What is the ratio of your result to the accepted value of the electron mass? (The result improves if more parts are assumed.)

Explanation / Answer

a)

U = 3*9e9*(1.6e-19/3)*(1.6e-19/3)/(2.82e-15) = 2.7234e-14 J

b)

2.7234e-14/3e8/3e8 = 3.026e-31 Kg

c)

3.026e-31/9.109e-31 = 0.332

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