The repulsive force between two particles of the same mass and charge, separated by a certain distance, is equal to the weight of one of them. The distance between them is ×10⁻¹ m. (Mass of particle = 1.66×10⁻²⁷ kg, charge of particle = 1.6×10⁻¹⁹ C, K = 9×10⁹ N m² C⁻², g = 10 m s⁻²)

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(4) 1.18. Given: m = 1.66×10⁻²⁷ kg, q = 1.6×10⁻¹⁹ C, K = 9×10⁹ N m² C⁻², g = 10 m s⁻². Idea: set the Coulomb repulsion equal to the weight of one particle, (Kq²)/(r²) = mg, so r = q√K/(mg). mg = 1.66×10⁻²⁷×10 = 1.66×10⁻²⁶ N K/(mg) = (9×10⁹)/(1.66×10⁻²⁶) = 5.42×10³⁵, so √K/(mg) = 7.36×10¹⁷ r = (1.6×10⁻¹⁹)(7.36×10¹⁷) = 0.1178 m = 1.178×10⁻¹ m So the blank is 1.18: the distance is 1.18×10⁻¹ m.

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