Highly excited state for hydrogen - like atom (also called rydberg states) with nuclear charge Ze are defined by their principal quantum number n, where `ngtgt1` Which of the following statement is (are) true?

Options

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`

Answer

A, B, D

Explanation

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`