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:

As we know, `v = nlambda`,
`rArr 1/lambda = n/v rArr 1/lambda = R ((1)/(n_(1)^(2))- 1/(n_(2)^(2)))`
`rArr v = Rc ((1)/(n_(1)^(2)) - 1/(n_(2)^(2)))`
`:.`
`v_(2) = Rc((1)/(2^(2)) - 1/(3^(2))) = Rc (1/4 - 1/9)"…"(i)`
`v_(1) = Rc ((1)/(2^(2))) = (Rc)/(4)`
`v_(3) = Rc ((1)/(3^(2))) = (Rc)/(9)`
`rArr v_(1) - v_(3) = Rc (1/4 - 1/9)`
From Eqs. (i) and (ii), we get
`v_(1) - v_(3) = v_(2)`
`rArr 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)`