Name: Methods of Representing Electronic Configuration
Uploaded: 2019-07-19
Duration: 11 min 48 s
Description: The electron configuration of an atom is the representation of the arrangement of electrons distributed among the orbital shells and subshells. Learn more.

Question

What is the wave number and wave length of the first transition in the Lyman, Balmer and Paschen series in the atomic spectra of hydrogen?

Accepted Answer

General equation for wave number:

$⊽ = R_{H} [\frac{1}{n_{f}^{2}} - \frac{1}{n_{i}^{2}}] Z^{2}$

$R_{H} =$ Rydberg constant $= 1.097 \times 10^{7} m^{- 1}$

For hydrogen atom, $Z = 1$

Wave length is given by;

$λ = \frac{1}{⊽}$

Series First Transition

Lyman $n_{i} = 2 to n_{f} = 1$

Balmer $n_{i} = 3 to n_{f} = 2$

Paschen $n_{i} = 4 to n_{f} = 3$

The Lyman series is a hydrogen spectral series of transitions comes under ultraviolet region. The Balmer series is a hydrogen spectral series of transitions comes under visible region. The Paschen series is a hydrogen spectral series of transitions comes under infrared region.

Therefore, wave number and wave length for first transition in the Lyman series is given by:

$⊽ = 1.097 \times 10^{7} [\frac{1}{1_{}^{2}} - \frac{1}{2_{}^{2}}] = 8.23 \times 10^{6} m^{- 1} λ = \frac{1}{8.23 \times 10^{6}} = 1.21 \times 10^{- 7} m$

In Balmer series,

$⊽ = 1.097 \times 10^{7} [\frac{1}{2_{}^{2}} - \frac{1}{3_{}^{2}}] = 1.52 \times 10^{6} m^{- 1} λ = \frac{1}{1.52 \times 10^{6}} = 6.5 \times 10^{- 7} m$

In Paschen series,

$⊽ = 1.097 \times 10^{7} [\frac{1}{3_{}^{2}} - \frac{1}{4_{}^{2}}] = 5.33 \times 10^{5} m^{- 1} λ = \frac{1}{5.33 \times 10^{5}} = 1.88 \times 10^{- 6} m$

What is the wave number and wave length of the first transition in the Lyman, Balmer and Paschen series in the atomic spectra of hydrogen?

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