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प्रश्न
Discuss the spectral series of hydrogen atom.
उत्तर
- As electron in excited states have a very small lifetime, these electrons jump back to the ground state through spontaneous emission in a short duration of time (approximately 10) by emitting the radiation with the same wavelength (or frequency) corresponding to the colours is absorbed. This is called emission spectroscopy.
Spectral series – Lyman, Balmer, Paschen series - In each series, the distance of separation between the consecutive wavelengths decreases from higher wavelength to the lower wavelength, and also wavelength in each series approach a limiting value known as the series limit.
- The wavelengths of these spectral lines perfectly agree with the wavelengths calculate using an equation derived from the Bohr atom model.
`1/lambda = "R" (1/"n"^2 - 1/"m"^2) = bar"v"` ...(1)
where `bar"v"` is known as wave number which is inverse of the wavelength, R is known as Rydberg constant whose value is 1.09737 × 107 m-1 and m and n are positive integers such that m > n.
The various spectral series are discussed below:
- Lyman 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 the ultra-violet region is
`bar"v" 1/lambda (1/"n"^2 - 1/"m"^2) = bar"v"` - 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 the visible region is
`bar"v" 1/lambda "R"(2/"n"^2 - 1/"m"^2) = bar"v"` - 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 the infra-red region (near IR) is
`bar"v" 1/lambda "R"(3/"n"^2 - 1/"m"^3) = bar"v"` - Brackett series:
Put n = 4 and m = 5, 6, 7 ….in equation (1). The wave number or wavelength of spectral lines of Brackett series which lies in the infra-red region (middle IR) is
`bar"v" 1/lambda "R"(4/"n"^2 - 1/"m"^3) = bar"v"` - 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 the infra-red region (far IR) is
`bar"v" 1/lambda "R"(5/"n"^2 - 1/"m"^2) = bar"v"`
- Lyman series:
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