Hydrogen Emission Spectrum

The hydrogen spectrum is “multi-dimensional”, with “more than three lines” visible to the naked eye. Both the “ultraviolet” and “infrared” parts of the spectrum can be used to detect “patterns of lines”. These are divided into several “series” of lines, each named after the individual who found them, as detailed hereon. 

Three of these series are depicted in the diagram below, although others are in the infrared to the left of the Panchen series. A sequence of lines in the ultraviolet range is known as the Lyman series. As the frequency rises, the lines become closer and closer together. The shaded section on the right end of the sequence suggests this. The series comes to an end at a specific moment known as the series limit. The pattern is the same as the Balmer and Paschen series, but the series is more compact. Take note of the three visible lines from the shot farther up the page in the Balmer series.

Frequency and Wavelength

The hydrogen spectrum is frequently depicted using light wavelengths rather than frequencies. Unfortunately, when the spectrum is plotted against frequency or wavelength, two completely distinct views of the spectrum are obtained due to the mathematical relationship between the “frequency of light” and its “wavelength”.

The origin of the hydrogen emission spectrum

The lines in the hydrogen emission spectrum follow a regular pattern and can be represented by a (relatively) straightforward equation. A combination of basic whole integers can be used to calculate each line. What is the meaning of those entire numbers, and why does hydrogen emit light when activated by a high voltage?

However, if the atom is given energy, the electron gets stimulated to a higher energy level or perhaps ejected from the atom entirely. A discharge tube’s high voltage supplies such energy.

The significance of the “numbers” in the “Dr Rydberg equation”

The energy levels at each end of the leap create a particular line in the spectrum and are represented by n1 and n2 in the Rydberg equation. The level being jumped from is n2. n2 is equivalent to 3 in the scenario where electrons fall from the 3-level to the 2-level, resulting in a red line.

The significance of the infinity level

As a component of a hydrogen atom, the infinity level signifies the highest conceivable energy an electron can have. If the “electron’s energy” exceeds that of the atom, it is no longer a part of it. The “infinity level” denotes the point at which “an atom is ionised”, resulting in a “positively charged ion”.

Using the “spectrum” to find the “ionisation energy of hydrogen.”

The “electron” of a “hydrogen atom” is discovered at the “1-level” when no further energy is supplied to it. This is referred to as the “ground state”. The atom gets ionised when enough energy is supplied to propel the electron to the infinity level. The ionisation energy per electron thus measures the difference in energy between the 1-level and the infinity level. The particular energy jump results in the Lyman series limit. A drawback of this approach is that determining the frequency of a series limit from a spectrum is difficult since the lines are so close together in that region that the spectrum seems continuous.

Finding the frequency of the series limit graphically.

The rise in frequency decreases as the lines approach closer together. In reality, the data in the table above can be used to create two graphs. Two frequencies are involved in the frequency differential. For example, subtracting 2.467 from 2.924 yields a value of 0.457. It makes no difference whether the two values are displayed against 0.457 as long as consistency is maintained—the difference must always be plotted against the higher or lower figure.

Hydrogen emission spectrum diagram