show work 1046 Calculate the classical energy of an electron

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10.46 Calculate the classical energy of an electron and proton separated by 0.0529 nm, relative to the same system at infinite separation. Compare this with the quantum mechanical result for the energy.

Solution

potential energy of teh proton-electron system

U = kq²/r = 8.987e+9*(1.60e-19)²/0.0529e-9 = 435e-20 J

with quantum mechanics it is like hydrogen atom in ground state

E = 13.6 ev = 13.6*1.60e-19 J = 21.76e-19 J