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Question

Highly excited states for hydrogen-like atoms (also called Ryberg 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?

A
Relative change in the radii of two consequtive orbitals does not depend on Z.
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B
Relative change in the radii of two consequtive orbitals varies as 1/n.
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C
Relative change in the energy of two consequtive orbitals varies as 1/n3
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D
Relative change in the angular momenta of two consequtive orbitals varies as 1/n.
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Solution

The correct options are
A Relative change in the radii of two consequtive orbitals does not depend on Z.
B Relative change in the radii of two consequtive orbitals varies as 1/n.
C Relative change in the angular momenta of two consequtive orbitals varies as 1/n.
r=r0(n2z)

Δrr=2Δnn

Since Δn=1,

Δrrα1n

L=nh2π

ΔLL=Δnn

ΔLLα1n

Answer is ABD.

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