Hight excited state for hydrogen - like atom (also called rydherg quanitum number n, where ngtgt1 which of the following statement is (are) true?

Options

A. Relative change in the radil of two consecative orbiats does niot depend on `Z`
B. Relative change in the radil of two consecative orbiats varies as `1//n`
C. Relative change in the energy of two consecative orbiats varies as `1//n^(3)`
D. Relative change in the angular moments of two consecative orbiats varies as `1// n`

Answer

A, B, D

Explanation

we kniow that `r = r_(0) (n^(2))/(z) , V_(0) = (13.6z^(2))/(n^(2)) , L_(0) = (nh)/(2 pi) `
Relative change in the radii of conseutive orbitals
`(r_(0) - r_(e-1))/(r_(0)) = 1 - r_(e-1))/(r_(0)) = 1 - ((n - 1)^(2))/(n^(2))` does not depend no Z
`= (2n - 1)/(n^(2)) = (2)/(n) ( ," ngtgt 1 )`
`(E_(0) - E_(n-1))/(E_(0)) = 1 - (E_(e -1))/(E_(0)) = 1 - (n^(2))/((n - 1 )^(2)) = (-2n - 1 )/((n- 1)^(2)) = (-2)/(n)`
`(1_(0) - 1_(n -1))/(1_(0)) = 1 - 1 _(n-1))/(1_(0)) = 1 - ((n - 1))/(n) = (1)/(n) `