Calculate the frequency of the spectral line corresponding to`n(1) = 2` and `n_(2)= 4`. To which spectral series does this line belong ?

Explanation

`bar(v) = R((1)/(n_(1)^(2))-(1)/(n_(2)^(2)))`
`n_(1)=2`
`n_(2)=4`
`bar(v) = (1)/(lambda)`
R = Rydberg constant `= 109677`
Substituting thevalue in the equation
`(1)/( lambda) = 109677 ((1)/((2)^(2))-(1)/((4)^(2)))cm^(-1)`
`(1)/(lambda) =20564.43 cm^(-1)`
`lambda= 4.86 xx 10^(-5) cm`
`lambda= 4.86 xx 10^(-7) m`
Frequency `(v) = (c )/(lambda)`
`v= ( 3 xx 10^(8)ms^(-1))/(4.86 xx 10^(-7) m)`
`= 6.172 xx 10^(14)s^(-1)`
So, the frequency of spectral line is `6.172 xx 10^(14)s^(-1)`
Since, `n=2` , so it belongs to Balmer series.