InterviewSolution
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InterviewSolution
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Highly excited states for hydrogen like atom (alos called Ryburg states) with nucleus Charge Ze are defined by their principal qunatum number n, where `n lt lt 1`. Which of the following statement(s) is (are) true?A. Releative change in the radii of two consecutive orbitals does not depend on `Z`B. Relative change in the radii of two consecutive orbitals varies as `1//n`C. Relative change in the energy of two consecutive orbitals varies as `1//n^(2)`D. Relative change in the angular momenta of two consecutive orbitals varies as `1//n` |
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Answer» Correct Answer - A::B::D As radius `r prop n^(2)/z` `implies (Deltar)/r=(((n+1)/z)^(2)-(n/z)^(2))/((n/z)^(2))=(2n+1)/n^(2) ~~2/n prop 1/n` as energy `E prop z^(2)/n^(2)` `implies (DeltaE)/E=(z^(2)/n^(2)-z^(2)/((n+1)^(2)))/(z^(2)/((n+1)^(2)))=((n+1)^(2)-n^(2))/(n^(2).(n+1)^(2)).(n+1)^(2)` `implies (DeltaE)/E=(2n+1)/n^(2) cong (2n)/n^(2) prop 1/n` as angular momentum `L=(nh)/(2pi)` `implies (DeltaL)/(L)=(((n+1)h)/(2pi)-(nh)/(2pi))/((nh)/(2pi))=1/n prop 1/n` |
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