Suppose the charge of a proton and an electron differ slightly. One of them is $$-e$$, the other is (e+$$Δ$$e). If the net of electrostatic force and gravitational force between two hydrogen atoms placed at a distance d (much$$ greater than atomic $$size) apart is zero, then Δe is of the order of Given mass of hydrogen $$mh=1.67$$×$$10-27$$ kg

Question

Suppose the charge of a proton and an electron differ slightly. One of them is $$-e$$, the other is (e+$$Δ$$e). If the net of electrostatic force and gravitational force between two hydrogen atoms placed at a distance d (much$$ greater than atomic $$size) apart is zero, then Δe is of the order of Given mass of hydrogen $$mh=1.67$$×$$10-27$$ kg

Infinity Learn · Accepted Answer

A hydrogen atom consists of an electron and a proton.∴ Charge on one hydrogen atom $$=qe+qp=-e+(e+$$Δ$$e)=$$Δe Since a hydrogen atom carry a net charge Δe , ∴ Electrostatic force, $$Fe=14$$πε$$o($$Δ$$e)2d2$$            . . . .(i)will$$ act between two hydrogen atoms. The gravitational force between two hydrogen atoms is given $$asFg=Gmhmhd2$$                      . . . .$$(ii)Since$$, the net force on the system is zero, $$Fe=Fg$$ Using eqns.$$(i) and (ii), we $$get($$Δ$$e)24$$πε$$od2=Gmh2d2($$Δ$$e)2=4$$πε$$oGmh2=6.67$$×$$10-11$$×$$1.67$$×$$10-272/9$$×$$109$$Δe≈$$10-37C$$

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