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. Relative change in the radii of two consecutive orbitals does not depends 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^(3)`
D. Relative change in the angular momentum of two consecutive orbitals varies as `1//n`

Answer

A, B, D

Explanation

As radius, `r prop (n^(2))/Z`
`:. (Deltar)/r=((n+1)^(2)-n^(2))/(n^(2))=(2n+1)/(n^(2)) prop 1/n`
Choices (a) and (b) are correct.
As energy `E prop(Z^(2))/(n^(2))`.
`(DeltaE)/E=(1/(n^(2))-1/((n+1)^(2)))/(1//(n+1)^(2))=((n+1)^(2)-n^(2))/(n^(2)(n+1)^(2))(n+1)^(2)`
`(DeltaE)/E=(2n+1)/(n^(2)) prop 1/n`.
Choice (c) is incorrect.
Angular momentum, `L=(nh)/(2pi)`
`(DeltaL)/L=((n+1)h-nh)/(nh)=1/n :. (DeltaL)/L prop 1/n`
Choice (d) is correct.