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?

Options

A. Relative 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_3`
D. Relative change in the angular momentum of consecutive orbitals varies as 1/n

Answer

A, B, D

Explanation

Orbital radius is proportional to `n^2`
`r_n=kn^2`
`(Deltar)/r_n=((n+1)^2-n^2)/n^2=(1+1/n)^2 -1 approx 2/n`
Hence option (a) and (b) are correct .
Energy of `n^(th)` orbit for hydrogen-like atoms is given by `E_n=(-13.6Z^2)/n^2` eV
Relative change in energy for two consecutive orbits can be written as follows :
`(E_(n+1)-E_n)/E_n=((-13.6Z^2/((n+1)^2))-(-13.6Z^2/n^2))/((-13.6Z^2/n^2))approx -2/n`
hence option (c) is wrong.
Further angular momentum is given by the following relation :
`L=nh/(2pi)`
`rArr (DeltaL)/L_n=((n+1)-n)/n=1/n`