Line Spectra of the Hydrogen Atom

Introduction
The line spectra of the hydrogen atom refers to the distinctive pattern of wavelengths or colors emitted or absorbed by hydrogen gas when it undergoes a transition between energy levels. These line spectra provide crucial information about the energy levels and electronic structure of the hydrogen atom.

Atomic Structure of Hydrogen
The hydrogen atom consists of a single proton in the nucleus and one electron orbiting around it. The electron can occupy different energy levels, represented by quantum numbers. The lowest energy level, called the ground state (n=1), is closest to the nucleus, while higher energy levels are further away.

Emission and Absorption of Energy
When an electron in the hydrogen atom absorbs energy, it jumps from a lower energy level to a higher energy level, called an excited state. This absorption of energy corresponds to a specific wavelength or color of light. Conversely, when an electron in an excited state returns to a lower energy level, it emits energy in the form of light of a specific wavelength.

Line Spectra
The line spectra of the hydrogen atom consist of discrete lines of light at specific wavelengths. Each line corresponds to a transition between two energy levels of the atom. The wavelengths of these lines can be calculated using the Rydberg formula:

1/λ = R * (1/n₁² - 1/n₂²)

where λ is the wavelength, R is the Rydberg constant, and n₁ and n₂ are the initial and final energy levels, respectively.

Visible Balmer Series
One of the most prominent line spectra of hydrogen is the Balmer series, which consists of visible light wavelengths. The Balmer series corresponds to transitions where the electron starts in an energy level higher than the ground state (n>1) and ends in the first excited state (n=2). The visible lines in the Balmer series include the red (n₁=3 to n₂=2), blue-green (n₁=4 to n₂=2), and violet (n₁=5 to n₂=2) lines.

Ultraviolet Lyman Series
Another important line spectra of hydrogen is the Lyman series, which lies in the ultraviolet region of the electromagnetic spectrum. The Lyman series corresponds to transitions where the electron starts in an energy level higher than the ground state (n>1) and ends in the ground state (n=1). The ultraviolet lines in the Lyman series include the Lyman alpha (n₁=2 to n₂=1), Lyman beta (n₁=3 to n₂=1), and Lyman gamma (n₁=4 to n₂=1) lines.

Infrared Paschen Series
The Paschen series is a line spectra of hydrogen in the infrared region. It corresponds to transitions where the electron starts in an energy level higher than the ground state (n>2) and ends in the second excited state (n=3). The infrared lines in the Paschen series include the Paschen alpha (n₁=4 to n₂=3), Paschen beta (n₁=5 to n₂=3), and Paschen gamma (n₁=6 to n₂=3) lines.

Conclusion
The line spectra of the hydrogen atom are a result of the quant