Discuss the spectral series of hydrogen atom.

Explanation

The spectral lines of hydrogen are grouped in separate series. In each series , the distance of separation between the consecutive wavelengths decreases from higher wavelength to the lower wvaelength, and also wavelength in each series approach a limiting value known as the series limit. Thses series are named as Lyman series, Balmer series ,Paschen series, Brackett series.Pfund series. etc. The wavelengths of these spectral lines perfectly agree with the equation derived from Bohr atom model.
`1/(lambda) = R((1)/(n^(2)) - (1)/(m^(2))) = overline v` ....(1)
where `overline v` is known as wave number which is inverse of wavelength, R is known as Rydberg constant whose value is `1.09737 xx 10^(7) m^(-1)` and m and n are positive integers such that `m gt n`.The various spectral series are discussed below:
(a) Layman series:
Put n = 1 and m = 2,3,4.....in equation(1). The wave number or wavelength of spectral lines of Lyman series which lies in ultra-violet region is
` overline v = (1)/(lambda) = R ((1)/(1^(2)) - (1)/(m^(2)))`
(b) Balmer series :
Put n = 2 and m = 3,4,5 ...in equation(1). The wave number or wavelength of spectral lines of Balmer series which lies in visible region is
` overline v = (1)/(lambda) = R((1)/(2^(2)) - (1)/(m^(2)))`
(c) Paschen series :
Put n = 3 and m = 4,5,6 ......in equation(1). The wave number or wavelength of spectral lines of Paschen series which lies in infra - red region (near IR) is
` overline v = (1)/(lambda) = R ((1)/(3^(2)) - (1)/(m^(2)))`
(d) Brackett series :
Put n = 4 and m = 5,6,7 ....in equation (1). The wave number or wavelength of spectral lines of Brackeet sereis which lies in infra-red region(middle IR) is
`overline v = (1)/(lambda) = R ((1)/(4^(2)) - (1)/(m^(2)))`
(e) Pfund series :
Put n = 5 and m = 6, 7, 8 ....in equation(1). The wave number or wavelength of spectral lines of Pfund series which lies in infra-red region(far IR) is
`overline v = (1)/(lambda) = R((1)/(5^(2)) - (1)/(m^(2)))`