Highly excited states for hydrogen –like atoms (also called Rydberg states) with nuclear charge Ze are defined by their principal quantum number n, where n>>1. Which of the following statement (s) is (are) true?

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Relative change in the radii of two consecutive orbitals does not depend on Z

Relative change in the radii of two consecutive orbitals varies as 1/n

Relative change in the energy of two consecutive orbitals varies as 1/n3

Relative change in the angular moment of two consecutive orbitals varies as 1/n

answer is A.

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Detailed Solution

(B) r=0.529n2zdrr=0.529[2n]dn/z0.529n2/z=2dnn For consecutive orbital's dn=1⇒drr∝1n (C) |E|=13.6Zn2dEE=(13.6)z(−2)n3dn13.6zn2=−2dnn, here dn=1∴dEE∝1n(D)L=nh2π⇒L∝n⇒dLL=dnn, here dn=1∴dLL∝1n

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