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 orbits does not depend on `Z`
B. Relative change in the radii of two consecutive orbits veries as `1//n`
C. Relative change in the energy of two consecutive orbits varies as `1//n^(3)`
D. Relative change in the angular momentum of two consecutive orbits varies as `1//n`

Answer

A, B, D

Explanation

as energy `Eprop(Z^(2))/(n^(2))`
`rArr (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)`
`rArr (DeltaE)/(E) = (2n + 1)/(n^(2)) = (2n)/(n^(2)) prop (1)/(n)`