The Zeeman effect is observed as a splitting in the spectral lines of hydrogen in the presence of a magnetic field. What is the greatest number of lines that a single spectral line can be split into by a magnetic field?

The Zeeman effect is a phenomenon where spectral lines of an atom or molecule split into multiple lines when subjected to a magnetic field. The number of lines that a single spectral line can be split into depends on the type of transition involved and the strength of the magnetic field.

In the case of the Zeeman effect, the number of lines that a single spectral line can be split into is determined by the magnetic quantum number. The magnetic quantum number, denoted by m, represents the orientation of the electron's magnetic moment with respect to the external magnetic field.

For a given spectral line, the number of possible values of the magnetic quantum number (m) determines the maximum number of lines that can be observed. The number of lines is given by 2m + 1, where m can take on integer values ranging from -l to +l.

In the case of hydrogen, the spectral lines are typically split into three components: the main central line, and two side lines. The main central line corresponds to m = 0, and the two side lines correspond to m = +1 and m = -1. Therefore, for hydrogen, a single spectral line can be split into a maximum of three lines.

However, it is important to note that the number of lines observed in practice can also depend on factors such as the resolution of the instrument used for observation and the strength of the magnetic field applied. Additionally, higher energy levels and more complex atoms can exhibit more lines due to additional transitions and interactions with the magnetic field.