The Bohr model of the hydrogen atom states that the single electroncan exist onl

Question

The Bohr model of the hydrogen atom states that the single electroncan exist only in certain allowed orbits around the proton. Theradius of each Bohr orbit is r = n2(0.0529 nm) where n = 1, 2, 3,... Calculate the electricpotential energy of a hydrogen atom for the following cases.Express your answer in electron volts. (a) when the electron is in the first allowedorbit, with n = 1
1 eV

(b) when the electron is in the second allowed orbit, n =2
2 eV

(c) when the electron has escaped from the atom, with r =
3 eV
(a) when the electron is in the first allowedorbit, with n = 1
1 eV

(b) when the electron is in the second allowed orbit, n =2
2 eV

(c) when the electron has escaped from the atom, with r =
3 eV

Explanation / Answer

E = -13.6eV / n^2 is the total energy... so if you want thepotential energy we have to subtract the kinetic. The electric potential energy is -ke^2/r and r=n^2 Rb So the electric potential is -ke^2/(n^2 0.0529 nm) =-4.355e-18 / n^2 Joules =-27.22eV/n^2 a) -27.22eV b) -6.81 eV c) 0 (n=infinity)

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