Calculate and the draw on the wavelength scale the spectral intervals in which the Lyman's Balmer,and Paschen serie for atomic hygeogen are confined. Show the visible portion of the specturm.

Explanation

From the general formula of the transition `n_(2)rarrn_(1)`
` ħ omega=E_(H)((1)/(n_(1)^(2))-(1)/(n_(2)^(2)))`
where `E_(H)= 13.65eV. Then
`(1)Lyman, `n_(1)=1,n_(2)=2,3` Thus
` ħ omega ge (3)/(4)E_(H)= 10.238eV`
This corresponds to `lambda=(2pi c ħ)/( ħ omega)= 0.121 mu m`
and Lyman lines have `lambdage 0.0121 mu m` with the series limit at `.0909 mu m`
(2)Balmer: `n_(2)=2,n_(3)= 3,4`
`ħ omega ge E_(H)((1)/(4)-(1)/(9))=(5)/(36)E_(H)= 1.876eV`
This corresponds to
`lambda= 0.65mu m`
and Balmer series has `lambda le 0.65mu m` with the series limit at `lambda= 0.363mu m`.
(3) Paschen : `n_(2)=3, n_(1)= 4,5`....
`h omega ge E_(H)((1)/(9)-(1)/(16))=(7)/(144)E_(H)=0.6635eV`
This corresponds to `lambda=1.869mum`
with the series limit at `lambda=0.818mu m`