What will be the ratio of the wavelength of the first line to that of the second line of paschen series of h atom?
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The first line in paschen series corresponds transition from n=4 to n=3 so wave length is given as,
(RH is Rydberg's constant )
1λ1=RH(1n21−1n22)
1λ1=RH(132−142)
1λ1=RH(19−116)
1λ1=RH(7144)
λ1=1447RH
The first line in paschen series corresponds transition from n=5 to n=3 so wave length is given as,
1λ2=RH(1n21−1n22)
1λ2=RH(132−152)
1λ2=RH(19−125)
1λ2=RH(16225)
λ2=RH(16225)
Now, ratio of two wavelength is given as,
λ1λ2=1447RH×16RH225
=256175 or 1.46