If `v_1` is the frequency of the series limit of lyman series, `v_2` is the frequency of the first line of lyman series and `v_3` is the frequency 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)`

Answer

A

Explanation

For lyman series
`upsilon=Rc[(1)/(1^2)-(1)/(n^2)]`
where n=2,3,4,.......
for the seires limit of lyman series , `n=oo`
`therefore upsilon_1=Rc[(1)/(1^2)-(1)/(oo^2)]=Rc`.........(i)
for the first line of lyman series, `n=2`
`therefore upsilon_2=Rc[(1)/(1^2)-(1)/(2^2)]=(3)/(4)Rc`........(ii)
for balmer series
`upsilon=Rc[(1)/(2^2)-(1)/(n^2)]`
where n= 3,4,5.....
For the series limit of balmer serie , `n=oo`
`thereforeupsilon_3=Rc[(1)/(2^2)-(1)/(oo^2)]=(Rc)/(4)`........(iii)
from equations (i),(ii),(iii), we get
`upsilon_1=upsilon_2+upsilon_3` or `upsilon_1-upsilon_2=upsilon_3`