The wavelength of the first line in the balmer series is `656 nm `. Calculate the wavelength of the second line and the limiting line in the Balmer series.

Explanation

According to Rydberg formula, `bar(v) = (1)/(lamda) = R ((1)/(n_(1)^(2)) - (1)/(n_(2)^(2)))`
For the Balmer series, `n_(1) = 2` and for the 1st line, `n_(2) = 3`
`:. (1)/(656) = R ((1)/(2^(2)) - (1)/(3^(2))) = R xx ((1)/(4) - (1)/(9)) = R xx (5)/(36) = (5R)/(36)`...(i)
For the second line,`n_(1) = 2, n_(2) = 4`
`:. (1)/(lamda) = R ((1)/(2^(2)) - (1)/(4^(2))) = R ((1)/(4) - (1)/(16)) = R xx (3)/(16) xx (3R)/(16)`...(ii)
Dividing eqn (i) by eqn. (ii) we get
`(lamda)/(656) = (5)/(36) xx (16)/(3) or lamda = 485.9 nm`
For the limiting line, `n_(1) = 2, n_(2) = oo`
`:. (1)/(lamda) = R ((1)/(2^(2)) - (1)/(oo^(2))) = (R)/(4)`....(iii)
Dividing eqn. (i) by eqn. (iii), we get
`(lamda)/(656) = (5)/(36) xx 4 or lamda = 364.4 nm`
Alternatively first calculate R from eqn. (i) and substitute in eqns (ii) and (iii)