An electron and a proton are placed a distance apart equal to one Bohr radius . We have to find the radius R of a lead sphere that must be placed directly behind the electron so that the gravitational force on the electron just overcomes the electrostatic attraction between the proton and the electron; see the figure. We may assume that the Newton’s law of gravitation holds, and that the density of the sphere equals the density of the lead on Earth.

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The magnitude of Coulomb force of attraction between the electron and the proton separated by one Bohr radius will be given by

where . We have

Let the radius of the lead sphere be R. The density of lead on Earth is . The magnitude of the force of gravitational attraction on the electron due to the mass of the spherical lead ball of radius R will be

Therefore, the radius R of a lead sphere that must be placed directly behind the electron so that the gravitational force on the electron just overcomes the electrostatic attraction between the proton and the electron will be given by requiring