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Which hydrogen ionic species has wavele...

Which hydrogen ionic species has wavelength difference between the first line of the balmer and first line of the lyman series equal to `859.3 xx 10^(-9)` m? Neglect the reduced mass effect.

Text Solution

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Wave number of first Balmer lien of an species with atomic number Z is given by
`barv.=RZ^(2)[1/(1^(2))-1/(2^(2))]`
`barv.=(5RZ^(2))/36,` Similarly wave number of `barv` of first Lyman line is given by
`v=RZ^(2)[1/(1^(2))-1/(2^(2))]=3/4RZ^(2),barv=1/(lamda)` and `barv.=1/(lamda.)`
`:.lamda.=lamda.=36/(5RZ^(2))=4/(3RZ^(2))=1/(RZ^(2))[36/5-4/3]=88/(15RZ^(2))`
`:.Z^(2)=88/(59.3xx10^(-9)xx16xx1.097xx10^(7))=9`or Z=3
`:.` Ionic species is `Li^(2+)`
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