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How much energy is required to ionise a...

How much energy is required to ionise a H - atom if the electron occupie ` n=5 ` orbit ? Compare your answer with the ionization energy of H-atom (energy required to remove the electron from ` nth` orbit ).

Text Solution

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`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.
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