Spectral lines of the Lyman and Balmer series do not overlap. Verify this statement by calculating the longest wavelength associated with the Lyman series and the shortest wavelength associated with the Balmer series (in \(\mathrm{nm}\) ).

The Lyman series is a set of ultraviolet spectral lines of hydrogen that are due to electron transitions from higher energy levels to the lowest energy level, which is the ground state (with quantum number, n = 1). These lines are emitted by hydrogen atoms when electrons fall into the first energy level from higher levels. To get the longest wavelength or lowest energy transition of the Lyman series, one must consider the transition from the first excited state (n = 2) to the ground state. Using the Rydberg formula, the longest wavelength (and thus lowest energy) of the Lyman series is found to be 121.54 nm, which falls within the ultraviolet range of the electromagnetic spectrum.

The significance of the Lyman series lies in its applications in astronomy and diagnostics, as it can help in identifying hydrogen gas and determining its properties in various celestial objects. This series was named after its discoverer, Theodore Lyman, who first observed these lines in 1906.

• Lyman-alpha line (transition from n = 2 to n = 1) is the most well-known and is widely used in various fields of research.
• Being in the ultraviolet range, the Lyman series lines are not visible to the naked eye and require special equipment to be observed.

On the other hand, the Balmer series consists of visible spectral lines of hydrogen that are due to electron transitions from higher energy levels to the second energy level (with quantum number, n = 2). These lines are quite notable because they are visible to the naked eye and have played a crucial role in the study of atomic structure and stellar spectra. The shortest wavelength in the Balmer series corresponds to the transition from infinity to the second level. According to the calculations using the Rydberg formula, this shortest wavelength is 364.56 nm, which is part of the visible spectrum, specifically within the range of red light.

Named after Johann Balmer who discovered this series in 1885, the Balmer series has importance in determining the composition of stars and galaxies.

• The Balmer-alpha line, also known as H-alpha (transition from n = 3 to n = 2), is particularly important in astronomy for studying star-forming regions.
• As the Balmer lines can be seen with optical telescopes, they are among the most studied spectral lines in astronomical spectroscopy.

Spectral lines are unique patterns of light that are observed when the light emitted or absorbed by a substance is viewed through a prism or a diffraction grating. They are like a fingerprint for identifying different elements or compounds. Spectral lines occur because electrons in atoms absorb or emit energy in discrete packets called photons, leading to transitions between energy levels characterized by specific wavelengths.

The distinct spectral lines observed in the Lyman and Balmer series demonstrate the quantized nature of electron energy levels in a hydrogen atom. The Rydberg formula is key in predicting these spectral lines, providing insights into the atomic structure.

• The visibility of spectral lines depends on the wavelength; some are visible while others require specialized instruments to detect.
• Spectral lines are not only crucial in identifying elements but also in determining physical conditions like temperature and pressure in stars and other celestial bodies.