Question

Which best describes the emission spectra of atomic hydrogen? (1) A series of only four lines. (2) A discrete series of lines of equal intensity and equally spaced with respect to wavelength. (3) Several discrete series of lines with both intensity and spacing between decreasing as the wave number increases within each series. (4) A continuous emission of radiation of all frequencies.

Short answer

Option (3) is correct.

Step-by-step solution

- Identify the Characteristics of Atomic Hydrogen Spectrum

Understand that the emission spectra of atomic hydrogen are characterized by discrete lines rather than a continuous spectrum. This is important for eliminating certain options.

- Consider the Number of Lines

Option (1) mentions only four lines. The hydrogen spectrum contains more than four lines in various series such as Balmer, Lyman, and others. Therefore, option (1) is incorrect.

- Consider Line Spacing and Intensity

Option (2) mentions lines of equal intensity and equally spaced. In atomic hydrogen, the intensity and spacing of the lines vary, so option (2) is also incorrect.

- Analyze Series Characteristics

Option (3) mentions several discrete series with both intensity and spacing decreasing as the wave number increases. This accurately describes the behavior of the Balmer, Lyman, and Paschen series in the hydrogen spectrum.

- Consider Continuous Spectrum

Option (4) describes a continuous emission of radiation at all frequencies which does not apply to the hydrogen emission spectra.

- Conclusion

Based on the analysis, option (3) correctly describes the emission spectra of atomic hydrogen.

Key concepts

Hydrogen Spectrum

The hydrogen spectrum is the pattern of light emitted by hydrogen atoms. When hydrogen atoms absorb energy, their electrons jump to higher energy levels. When these electrons return to lower energy levels, they release energy in the form of light. This light forms unique patterns, known as emission spectra.
The emission spectrum of hydrogen is composed of discrete lines, not a continuous spectrum. Each line corresponds to a specific wavelength of light emitted when an electron transitions between energy levels. The most well-known series in the hydrogen emission spectrum are the Lyman, Balmer, and Paschen series.

Balmer Series

The Balmer series is a part of the hydrogen emission spectrum visible to the human eye. Named after Johann Balmer, it occurs when an electron falls from a higher energy level (n > 2) to the n = 2 level.
The Balmer series consists of the following:

• Four visible lines with wavelengths from low to high: ~410 nm (violet), ~434 nm (blue), ~486 nm (blue-green), and ~656 nm (red)
• Additional ultraviolet lines

These spectral lines are significant because they help in understanding atomic structure and the behavior of electrons.

Lyman Series

The Lyman series is part of the hydrogen emission spectrum but lies in the ultraviolet (UV) region. Discovered by Theodore Lyman, it occurs when an electron falls from a higher energy level (n > 1) to the n = 1 level.
Key characteristics include:

• All lines are in the ultraviolet part of the spectrum
• Important lines in this series have wavelengths of around 121.6 nm and 102.6 nm

The Lyman series provides vital data for studying atomic structure, particularly in UV spectroscopy.

Paschen Series

The Paschen series belongs to the hydrogen emission spectrum but is located in the infrared region. Named after Friedrich Paschen, these lines form when an electron falls from a higher energy level (n > 3) to the n = 3 level.
Important features:

• The lines are in the infrared part of the spectrum
• Some key lines have wavelengths around 1875 nm, 1282 nm, and 1094 nm

The Paschen series is essential for infrared spectroscopy and provides insights into the energy transitions occurring at longer wavelengths.