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We do not have to know the distances because, If we equate the forces, GMm/r^2=KQq/r^2, since r is same, it gets cancelled. Therefore, the product GMm= the product KQq. Since the charges are equal, we get GMm=KQ^2, where M--> mass of earth, m--> mass of moon. You know what G is.
One atom of H has one proton, which has a +ve charge of magnitude 1.6x10^-19. Therefore, no of H atoms = Q/Qp , where Q--> charge calculated in (a) and Qp --> 1.6x10^-19
mass of one H atom is known, and therefore we can find mass of that many atoms.
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