5. How far apart the two electrons be, if the force
between them equals the weight of an electron? What
in case of protons?
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The weight of an object is equal to it’s mass multiplied by the gravitational field strength it experiences. On the surface of the earth that is very roughly 10 Newtons for every kilogram of mass. An electron weighs roughly 1x10^-30 kg, so it has a weight of roughly 1x10^-29 N.
The force between two charges is given by Coulomb’s law:
f=k∗q1∗q2r2
k is Coulomb’s constant and has a value of roughly 1x10^10 N⋅m^2⋅C^−2
Equating these, multiplying out all the known values and doing some very basic algebra gives us an separation of roughly 5 metres.
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