(1) The energy associated with the first orbit in the hydrogen atom is `-2.18xx10^(-18)J*"atom"^(-1)`. What is the energy associated with the fifth orbit?
(2) Calculate the radius of Bohr's fifth orbit for hydrogen atom.

Explanation

(1) Energy of first orbit `(E_(1))=-2.18xx10^(-18)J*"atom"^(-1)`.
WE know, that, energy of n-th orbit `(E_(n))=E_(1)xx(Z^(2))/(n^(2))`
`=-2.18xx10^(-18)xx(1^(2))/(n^(2))" "[because" For H-atom, Z=1"]`
Thus, energy of 5th-orbit `(E_(5))=-2.18xx10^(-18)xx(1^(2))/(5^(2))`
`=-8.72xx10^(-20)J""atom"^(-1)`
(2) bohr radius for n-th orbit of H-atom `(r_(n))=0.529xxn^(2)`Å[`because` From H-atom, Z=1]
`therefore`Borh radius of 5th orbit, `r_(5)=0.529xx5^(2)` Å`=13.225`Å