If shortest wavelength of H-atom in Balmer series is X then (i) What is the shortest wave length in Lyman series. (ii) What is the longest wave length in Paschen series.

If shortest wavelength of H-atom in Balmer series is X then (i) What i

1.	If shortest wavelength of H-atom in Balmer series is X then (i) What is the shortest wave length in Lyman series. (ii) What is the longest wave length in Paschen series.
Answer» (i) `(1)/(lambda)=Z^(2)R_(H)[(1)/(n_(1)^(2))-(1)/(n_(2)^(2))]` `lambda=[(1)/(Z^(2)R_(H))][(n_(1)^(2)n_(1)^(2))/(n_(2)^(2)-n_(1)^(2))]` Shortest wavelength correspond to maximum energy `(E=(hc)/(lambda))` hence transition must be `n_(2)=oo, n_(1)=2` `=[(1)/(n_(1)^(2))-(1)/(n_(2)^(2))]=((1)/(4))=(n_(1)^(2)n_(2)^(2))/(n_(2)^(2)-n_(1)^(2))=4` `x=((1)/(Z^(2)R_(H)))4=(4)/(R_(H))implies R_(H)=(4)/(x)` (a) For shortest wavelength Lyman series `n_(1)=1,n_(2)=oo` `lambda=((1)/(R_(H)))implieslambda=(x)/(4)` (b) For longest wavelength in Paschen series `n_(1)=3,n_(2)=4` `implies (n_(2)^(2)n_(1)^(2))/(n_(2)^(2)-n_(1)^(2))=(144)/(16-9)=[(144)/(7)]=lambda=((1)/(R_(H)))xx(144)/(7)=(x x 144)/(4xx7)=(36x)/(7)`

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If shortest wavelength of H-atom in Balmer series is X then (i) What is the shortest wave length in Lyman series. (ii) What is the longest wave length in Paschen series.

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