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Wave number of a spectral line in the Ly...

Wave number of a spectral line in the Lyman series of H-atom is 82260 `cm^(-1)`. Show that this line has appeared in this series due to the return of the electron from the second to the first orbit.

Text Solution

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Wave number, `overline(v)=R[(1)/(n_(1)^(2))-(1)/(n_(2)^(2))]` [R=Rydberg's constant]
`therefore overline(v)=R[1-(1)/(n_(2)^(2))] or, (overline(v))/(R)=1-(1)/(n_(2)^(2))` [For Lyman series `n_(1)=1`]
or, `(1)/(n_(2)^(2))=1-(overline(v))/(R)=1-(82260)/(109680)=(27420)/(109680)=(1)/(4)=(1)/(2^(2))" "thereforen_(2)=2`
This means that, the electron has returned from the second to the first orbit.
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