Which of the following option(s) is/are independent of both `n` and `Z` for `H-`like species?
`U_(n) =` Potential energy of electron in `n^(th)` orbit
`KE_(n) =` Kinetic energy of electron in `n^(th)` orbit
`l_(n) =` Angular momentam of electoron in `n^(th)` orbit
`v_(n) =` Velcity of electron in `n^(th)` orbit
`f_(n) =` Frequency of electron in `n^(th)` orbit
`T_(n) =` Time period of revolution of electron in `n^(th)` orbit

Options

A. `(r_(n))/(U_(n))`
B. `r_(n) xx KE_(n) xx l_(n)`
C. `(U_(n) xx T_(n))/(l_(n))`
D. `(l_(n) xx f_(n))/(v_(n)^(2))`

Answer

C, D

Explanation

`(r_(n))/(U_(n))=((r_(0)n^(2))/(Z))/(-2E_(0)(Z^(3))/(n^(2))) = (r_(0))/(-2E) (n^(4))/(Z^(3))`
`r_(n).KE_(n).l_(n)=(r_(0)n^(2))/(Z)xx(E_(0)Z^(3))/(n^(2))xx(nh)/(2pi)=(r_(0)E_(0Znh))/(2pi)`
`(U_(n)xxT_(n))/(l_(n))=((-2E_(0)Z^(3))/(n^(2))xxT_(0)(n^(3))/(Z^(2)))/((nh)/(2pi))=(-2E_(0)T_(0))/(h)xx2pi`
`(l_(n)xxt_(n))/(v_(n^(2)))=((nh)/(2pi)xxf_(0)xx(Z^(2))/(n^(3)))/((v_(0)(Z)/(n))^(2)) =(hf_(0))/(2piv_(0)^(2))`