Let `v_(1)` be the frequency of series limit of Lyman series, `v_(2)` the frequency of the first line of Lyman series and `v_(3)` the frequency of series limit of Balmer series. Then which of the following is correct ?

Options

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

Answer

A

Explanation

`V=nlambda (1)/(lambda)=n/V`
`1/lambda=R((1)/(P^(2))-(1)/(n^(2)))`
`v=Rc ((1)/(P^(2))-(1)/(n^(2)))`
`v=Rc ((1)/(P^(2))-1/(n^(2)))" series limit n"=oo`
`v_(2)=Rc ((1)/(2^(2))-(1)/(3^(2)))=Rc=((1)/(4)-(1)/(9))`
`v_(1)=Rc((1)/(2^(2))=(Rc)/(4))`
`v_(3)=Rc((1)/(3^(2))=(Rc)/(9))`
`therefore v_(1)-v_(3)=Rc((1)/(4)-(1)/(9))`
`therefore v_1-v_3=v_2`
`therefore v_1-v_2=v_3`.