If `v_1` is the frequency of the series limit of lyman seies, `v_2` is the freqency of the first line of lyman series and `v_3` is the fequecny of the series limit of the balmer series, then

Options

A. `v_(1)-v_(2)=v_(3)`
B. `v_(1)=v_(2)-v_(3)`
C. `1/(v_(2))=1/(v_(1))+1/(v_(3))`
D. `1/(v_(1))=1/(v_(2))+1/(v_(3))`

Explanation

For Lyman series
`v=Rc[1/((1)^(2))-1/(n^(2))],n=2,3,4`…………
For the series limit for lyma series `n=oo`
`:'v_(1)=Rc[1/((1)^(2))-1/((oo)^(2))]=Rc`…….1
For the first line of lyman series n=2
`:.v_(2)=Rc[1/((1)^(2))-1/((2)^(2))]=3/4Rc` (2)
For Balmer series
`:.v=Rc[1/((2)^(2))-1/(n^(2))]=n=3,4,5`............
For the series limit of Balmer sereis `n=oo`
Similarly as eq (1)
`:.v_(3)=Rc[1/((2)^(2))-1/((oo)^(2))]=(Rc)/4`.....3
From eq 1, 2, and 3 we get
`v_(1)=v_(2)+v_(3)`
`impliesv_(1)-v_(2)=v_(3)`