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Determine the wavelength and frequency o...

Determine the wavelength and frequency of the radiation having the longest wavelength in Lyman series of hydrogen atom.

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Rydber's equation, `(1)/(lamda)=R[(1)/(n_(1)^(2))-(1)/(n_(2)^(2))]`, in case of Lyman series `n_(1)=1 &n_(2)=2` or any other higher intergram values (3, 4, 5 etc). For the wavelength to be the longest, the difference in energies between the two enerrgy levels should be minimum.
Hence, `n_(2)=2`
`therefore (1)/(lamda)=109678((1)/(1^(2))-(1)/(2^(2))) or, (1)/(lamda)=109678(1-(1)/(4))`
`therefore lamda=(4)/(3xx109678)=1215.67xx10^(-8)cm=1215.67` Å
So, the radiation having the longest wavelength in the Lyman series`=1215.67xx10^(-8)`cm.
`therefore`Frequency o the radiation,
`v=(c)/(lamda)=(3xx10^(10))/(1215.67xx10^(-8))s^(-1)=2.467xx10^(15)s^(-1)`.
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