2.18 In a hydrogen atom, the electron and proton are bound at a distance of about 0.53 \dot{A}

(a) Estimate the potential energy of the system in eV, taking the zero of the potential energy at an infinite separation of the electron from proton 

Answers (1)

As we know,

the distance between electron-proton of the hydrogen atom 

d=0.53*10^{-10}m 

The potential energy of the system = potential energy at infinity - potential energy at distance d

PE=0-\frac{ke*e}{d}=-\frac{9*10^9(1.6*10^{-19})^2}{0.53*10^{10}}=-43.7*10^{-19}J

As we know,

1ev=1.6*10^{-19}J

PE=\frac{-43.7*10^{-19}}{1.6*10^{-19}}=-27.2eV

Hence potential energy of the system is -27.2eV.

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