(i) The energy associated with first orbit in hydrogen atom is `-2.17xx10^(-18)J "atom"^(-1)` . What is the energy associated with the fifth orbit ?
(ii) Calculate the radius of Bohr's fifth orbit for hydrogen atom.

Explanation

(i) For an electron, the energies in two orbits may be compared as :
`(E_(1))/(E_(2))=((n_(2))/(n_(1)))^(2) " " [:'E_(n)prop (1)/(n^(2))]`
According to available data : `n_(1)=1, E_(1)=-2.17 xx 10^(-18) J "atom"^(-1), n_(2)=5`
`:.((-2.17 xx 10^(-18) J "atom" ^(-1)))/(E_(2))=((5)/(1))^(2)=25`
or `" " E_(5)=((-2.17xx10^(-18) J "atom" ^(-1)))/(25)=-8.77 xx10^(-20) J "atom"^(-1)`.
(ii) For hydrogen atom , `r_(n)=0.529 xx n^(2) Ã…`
`r_(5)=0.529 xx (5)^(2)=13.225 Ã…=1.3225 nm`.