For the Thomson atomic model for He(Z=2), two electrons (at rest) are embedded i

Question

For the Thomson atomic model for He(Z=2), two electrons (at rest) are embedded inside a uniform sphere having a positive charge of +2e. a) Sketch the situation b) Apply Gauss Law to find the electric field inside the sphere considering only the positive sphere (and thus not the two e's). c) Construct a free-body (force) diagram for one of the electrons inside the atom. d) Determine upper-and-lower-limits for the distance d(if any) between the electrons, such that this system is in static equilibrium. e) Using your results of b) and c) and plausible arguments, find this distance d between the two embedded electrons.

Explanation / Answer

ans D) electric field inside a uniformaly solid sphere of radius R at adistance r from the centre is given by
E = kQr / R3 (Q is total charge in the sphere )
in this question if electron is in equilibrium then force onelectron due to another electron is balanced by force due touniformally charged sphere
so
kee / d2 = k(2e)e*d / 2 (R)3 ( Q = 2e)
so d = R

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