The wavelength of the first line in the balmer series is 656 nm . Calculate the wavelengthof thesecond lineand the limitingline in the Balmer series.

The wavelength of the first line in the balmer series is 656 nm . Calc

1.	The wavelength of the first line in the balmer series is 656 nm . Calculate the wavelengthof thesecond lineand the limitingline in the Balmer series.
Answer» SOLUTION :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)