InterviewSolution
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InterviewSolution
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In a hydrogen atom , the electron and proton are bound at a distance of about 0.53Å. (a) Estimate the potential energy of the system in e V, taking the zero of the potential energy at infiniate separation of the electron from proton. (b) What is the minimum work required to free the electron, given that is kinetic energy in the orbit is half the magnitude of potenital energy obtained in (a) ? (c) What are the answers to (a) and (b) above if the zero of potential energy is taken at 1.06Å separation ? |
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Answer» Solution :Here `q_(1) = - 1.6 xx 10^(-19) C`, `q_(2) = + 1.6xx 10^(-19) C`. `r = 0.53 lambda = 0.53 xx 10^(-10) m` Potential energy = P.E at `prop` - P. E at r `= 0 - (q_(1) q_(2))/(4 pi r epsilon_(0) r) = (- 9 xx 10^(9) (1.6 xx 10^(-19))^(2))/(0.53 xx 10^(-10))` `= - 43.47 xx 10^(-19)` Joule `= (-43.47 xx 10^(-19))/(1.6 xx 10^(-19)) eV = - 27.16 eV`. (b) K.E in the orbit `= (1)/(2) (27.16) eV` Total energy = K.E + P.E = 13.58 - 27.16 = - 13.58 eV WORK required to free the electron = 13.58 eV Potential energy at a seperation of `r_(1) (= 1.06 Å)` is `= (q_(1) q_(2))/(4 pi epsilon_(0) r_(1)) = (9 xx 10^(9) (1.6 xx 10^(-19)))/(1.06 xx 10^(-10))` `= 21.73 xx 10^(-19) J = 13.58 eV` Potential energy of the system, when zero of P.E is taken at `r_(1) = 1.06Å` is = P.E at `r_(1)` - P.E at r = 13.58 - 27.16 = - 13.58 eV By shifting the zero of petential energy work required to free the electron is not affected. It CONTINUES to be the same, being equal to + 13.58 eV. |
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