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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 ?

A

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

B

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

C

`upsilon_(3)=1/2(upsilon_(1)+upsilon_(2))`

D

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

Text Solution

Verified by Experts

The correct Answer is:
A
Series limit means the shortest possible wavelength (maximum photon energy) and first line means the largest possible wavelength (minimum photon energy) in the series.
`" "upsilon=R[1/n^(2)-1/m^(2)]" (where R is a constant)"`
For series limit of Lyman series:
`" "n=1, m=infty rArr upsilon_(1)=R" ...(i)"`
For first line of Lyman series:
`" "n=1, m=2 rArr upsilon_(2)=3R//4" ...(ii)"`
For series limit of Balmer series:
`" "n=2, m=infty rArr upsilon_(3)=R//4" ...(iii)"`
From eqns. (i), (ii) and (iii),
`" "upsilon_(1)-upsilon_(2)=upsilon_(3)`
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