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

Since, `f= Rc [(1)/(n_(1)^(2))- (1)/(n_(2)^(2))]`
For series limit of Lyman, `[n_(1)= 1, n_(2)= oo]`
`f_(1)= v_(1) = Rc ((1)/(1)- (1)/(oo))= Rc`
For `1^(st)` line of Lyman, `[n_(1)= 1, n_(2)= 2]`
`f_(2)= v_(2) = Rc ((1)/(1^(2))- (1)/(2^(2)))= (3)/(4) Rc`
For series limit of Balmer, `pn_(1)= 2, n_(2) = oo]`
`f_(3)= v_(3) Rc [(1)/(4)- 0]= (Rc)/(4)`
`therefore v_(1) = v_(2) + v_(3) rArr v_(1)- v_(2)= v_(3)`