Answer :

Given,


The distance between electron-proton of hydrogen atom = 0.53 Å = 0.53 × 10-10m


Charge on electron, q1 = - 1.6 × 10-19 C


Charge on proton, q2 = 1.6 × 10-19 C


(a) Potential energy at infinity is Zero.


Potential energy of a system,


= Potential energy at infinity – Potential energy at distance d


= 0 -


Where, ϵ0 = permittivity of space


and, =


Potential energy,


V = -43.7 × 10-19 J


On converting into electron volts we get,



V = -27.2 eV


( 1eV = 1.6 × 10-19 J)


(b) Given, Kinetic energy is half of the potential energy in (a).


Kinetic energy, K = 0.5 × (27.2) = 13.6 eV


Thus, Total energy of electron = -27.2 + 13.6 = -13.6 eV


Amount of work require to free the electron, A = Increase in energy the electron.


A = 0-(-13.6) = 13.6 eV


(c) If we take potential energy Zero at 1.06 Å separation, then the potential energy of the system,


P =


P = -21.74 × 10-19 J


In electron volts, the potential energy is given as,


P = -13.585 eV.


(1eV = 1.6 × 10-19 J)


The amount of work done to free the electron in this case,


W = -27.17- (-13.585) = -13.585 eV


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