The Bohr model of the hydrogen atom states that the single electron can exist on

Question

The Bohr model of the hydrogen atom states that the single electron can exist only in certain allowed orbits around the proton. The radius of each Bohr orbit is r = n2 (0.0529 nm) where n = 1, 2, 3,... Calculate the electric potential energy of a hydrogen atom for the following cases. Express your answer in electron volts.

(a) when the electron is in the first allowed orbit, with n = 1
___?_____eV

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

(c) when the electron has escaped from the atom, with r =
___?_____eV

Explanation / Answer

E = -13.6eV / n^2 is the total energy... so if you want the potential 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

when n=1

=-27.22eV/n^2

a) -27.22eV

b) -6.81 eV

c) 0 (n=infinity)

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