Let v(1) be the frequency of series limi...

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 ?

`v_(1)-v_(2)=v_(3)`

`v_(1)+v_(3)=v_(2)`

`v_(1)+v_(2)=v_(3)`

`v_(1)-v_(3)=2v_(1)`

Text Solution

Verified by Experts

The correct Answer is:

`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`.

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Let v_(1) be the frequency of the series limit of the lyman series v_(2) be the frequency of the first line of th elyman series and v_(3) be the frequency of the series limit of the Balmer series

`nu_(1)` - `nu_(2)` = `nu_(3)`

`nu_(2)` - `nu_(1)` = `nu_(3)`

`nu_(2)` = `1/2( nu_(1) - nu_(3))`

`nu_(1)` + `nu_(2)` = `nu_(3)`

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

`v_1-v_2=v_3`

`v_1=v_2-v_3`

`(1)/(v_2)=(1)/(v_1)+(1)/(v_3)`

`(1)/(v_1)=(1)/(v_2)+(1)/(v_3)`

If v_1 is the frequency of series limit of Lyman series , v_2 is the frequency of the series limit of Balmer series. The

`v_1+v_2=v_3`

`v_2-v_1=v_3`

`v_1-v_2=v_3`

`v_3=1/2(v_1+v_2)`