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The atomic spectrum of Li^(2+) arises du...

The atomic spectrum of `Li^(2+)` arises due to the transition of an electron from `n_(2)` to `n_(1)` level. If `n_(1) +n_(2) ` is 4 and `n_(2)-n_(1)` is 2, calculate the wavelength (in nm) of the transition for this series in `Li^(2+)`

Text Solution

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Step I. Calculation of value of `n_(1)` and `n_(2)`
According to available information,
`n_(1)+n_(2)=4` and ` n_(2)-n_(1)=2`
On adding , ` 2n_(2)=6 " or " n_(2) =3` and ` n_(1)=4-3=1`.
Step II. Calculation of wavelength of transition
According to Rydberg formula,
`(1)/(lambda)=bar(v)=R_(H)Z^(2)((1)/(n_(1)^(2))-(1)/(n_(2)^(2))) , R_(H)=109678 cm^(-1) , Z(Li^(2+))=3, n_(1)=1, n_(2)=3`
`:. " " (1)/(lambda) =(109678 cm^(-1))xx(3)^(2) ((1)/(1^(2))-(1)/3^(2))=(109678 cm^(-1)) xx 9 xx(8)/(9)= 877424 cm^(-1)`
`lambda =(1)/((877424 cm^(-1)))=(1.14 xx 10^(-6)cm)= 1.14 xx 10^(-6) xx (1)/(10^(-7))=11.4 nm." " ` (`:. 1 nm=10^(-7)`cm)
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