how much energy is required to ionise a H atom if the electron occupies n=5 orbitl? Compare answer with the ionization enthalpy of H atom ( energy required to remove the electron from n=1 orbit)

Explanation

`E_(n)=-(21.8xx10^(-19))/(n^(2))"J atom"^(-1)`
For ionization from `5^("th")` orbit, `n_(1)=5, n_(2)=oo`
`=Delta E=E_(2)-E_(1)=-21.8xx10^(-19)((1)/(n_(2)^(2))-(1)/(n_(1)^(2)))=21.8xx10^(-19)((1)/(5^(2))-(1)/(oo^(2)))=8.72xx10^(-20)J`
For ionization from `1^("st")` orbit, `n_(1)=1, n_(2)=oo`
`DeltaE'=21.8xx10^(-19)((1)/(1^(2))-(1)/(oo))=21.8xx10^(-19)J" "(DeltaE)/(DeltaE)=(21.8xx10^(-19))/(8.72xx10^(-20))=2.5`
Thus, the energy required to remove electron from `1^("st")` orbit is 25 times than that required to remove electron from 5th orbit.