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The Lyman series of the hydrogen spectru...

The Lyman series of the hydrogen spectrum can be represented by the equation `v = 3.2881 xx 10^(15)s^(-1)[(1)/((1)^(2)) - (1)/((n)^(2))] [where n = 2,3,…….)`
Calculate the maximum and minimum frequencies of the lines in this series

Text Solution

Verified by Experts

`barv=1/(lamda)=1/v=(3.2881xx10^(15))/(3xx10^(8))m^(-1)[1/((1)^(2)-1/(n^(2)))]`
Wavelength is maximum `(barv_("min"))` when n is minimum so that `1/(n^(2))` is maximum.
`:.barv=1/(lamda_("max"))=(3.2881xx10^(15))/(3xx10^(8))[1/((1)^(2) )-1/((2)^(2))]`
`:.lamda_("max")=(3xx10^(8))/(3.2881xx10^(15))xx4/3`
`=1.2165xx10^(-7)m=121.67` min
Wavelength is minimum `(barv_("max"))` when n is `oo`
i.e. series converge
`v_("max")=1/(lamda_("min"))=(3.2881xx10^(15))/(3xx10^(8))`
`:.lamda_("min")=0.9124xx10^(-7)m 91.24nm`
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