(i) Which is highest frequency photon that can be emitted from hydrogen atom? What is wavelength of this photon?
(ii) Calclate the longest wavelength transition in the Pashen series of `He^(+)`.
(iii) Calculate the ratio of the wavelength of first and the ultimate line of Balmer sereis of `Li^(2+)`?

Explanation

(i) Highest frequency photon is emitted when electron comes from infinity to 1st energy level.
`E=-(13.6z^(2))/(1^(2))=-13.6eV`
or `13.6xx1.6xx10^(-19)` Joule `=2.76xx10^(-18)` Joule
`E=hv`
`:.v=E/h=(2.176xx10^(-18)J)/(6.626xx10^(-34)Js)=0.328xx10^(18)Hz`
`v=c/(lamda):.lamda=(3xx10^(80))/(0.328xx10^(16)Js)=9.146xx10^(-8)m`
(iii) `barv=R_(H)xxZ^(2)[1/(n_(1)^(2))-1/(n_(2)^(2))]`
For He Z=2, For Paschen series `n_(1)=3`
For longest wavelength `n_(2)=4`
`1/(lamda)=109678xx(2)^(2)xx[1/(3^(2))-1/(4^(2))]=109678xx4xx[1/9-1/16]=109678xx4xx7/144`
`lamda=4689Å`
(iii) Wave number of first line of Balmer,
`barv_(1)=RZ^(2)[1/(2^(2))-1/(3^(2))]=(5xx9r)/36=(5R)/4`
Wavelength of first line of Balmer `=4/(5R)`
Wave number of ultimate line of Balmer `barv_(2)=RZ^(2)[1/(2^(2))-1/(oo)]=(9R)/4`
`:.` Wavelength of ultimate of Balmer `=4/(9R)`
`:.` Ratio `=9/5`