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# Spectral Series

**Introduction**

In accordance with a general conceptualisation, spectral series are referred to as a set of parallel lines that represent uniform speed and distance. In such cases, it has been observed that the wavelength of light can create a significant impact on the wavelength of these spectral lines. Based on this basic conviction, the present tutorial will define the spectral series of Hydrogen atoms. Moreover, the tutorial will include the formation of the spectral series along with the explanation of the Rydberg formula.

## Spectral Series: Definition

**Figure 1: Spectral series**

The easiest way of understanding the principle of the spectral series is considered the study of hydrogen atoms. The most basic atomic system found in nature is Hydrogen with one electron and one portion. An image forms whenever the light or radiation enters a device with a slit. This picture can be observed with the help of a spectroscope (Du et al. 2021). The spectral lines, formed by the wavelength of the light, are arranged in a parallel form next to each other with consistent spacing.

## Formation of Spectral Series

**Figure 2: Formation of Spectral Series**

In order to understand the formation of the spectral series, Bohr's atomic model is generally used.

Being applied to the classical electromagnetic theory, this model is used in order to explain the set of energy levels that has been enclosed by each atom (McGuire et al. 2021).

Energy states are generally named on the basis of the quantum numbers. A release of a photon with energy nh – nl is observed in the time when electrons jump to a lower energy state (nl) from a higher energy one (nh).

The production of the same energy phonon is witnessed in time when a transition happens within two energy states that are similar to each other because the associated energy in every state is fixed which helps to divide the spectral series into an equivalent series.

## Rydberg formula

**Figure 3: Rydberg formula**

The atomic Hydrogen is considered responsible for putting on the view of The emission spectrum. This specific spectrum is found to be made up of different numerical spectral series.

Once, the energy levels reach the excited state, a transition between energy levels is observed in the electrons of Gas. The wavelength of the spectral series can be calculated by the use of the Rydberg formula (En.universaldenker, 2022).

The difference between energy levels that are observed in Bohr's model and the wavelengths of the spectral lines of the emitted photon is generally represented by the mathematical representation of Rydberg formula.

The mathematical representation of this formula is $\mathrm{\frac{1}{\lambda}=RZ^{2}(\frac{1}{n_1^{2}} −\frac{1}{n_2^{2}})}$. In this formula, the letter R is considered Rydberg constant with the value of 1.0973710^{7} m^{-1}. λ represents wavelength and Z is the atomic number.

## Types of Spectral Series

### Lyman series

This particuler series is named after Theodore Lyman as he was the founder of that series. In accordance with Bohr's model, when transitioning of electoral is observed to the level of nl = 1 from higher energy states, the appearance of the Lyman series can be seen (Quimby et al. 2018).

### Balmer series

Johann Balmer generally founds this specific series in the year 1885. The occurrence of the Balmer series can be observed in the time of shifting electrons from the energy level that is higher to the lower energy state (nl = 2) that are visible in the spectrum of electron (400nm to 740nm).

### Paschen series

The name of series is named after Friedrich Paschen who found this spectrum in the year 1908. At the time of migration of the electrons to the lower energy states (nl = 3) from higher energy levels are considered as Paschen series (Ucolick, 2022). The wavelength of this series is in the infrared range of the electromagnetic spectrum.

### Brackett series

Friedrich Sumner Brackett founds this specific series in the year 1922 therefore, this series is named after him. At the time when the electrons are started shifting from a higher energy state towards a lower one, the Brackett series appears.

### Pfund series

This series is named after August Harman Pfund and it occurs when the electrons migrate to a lower energy state (nl = 5). The wavelength of this series is in all infrared part of the spectrum that is considered as electromagnetic.

### Humphrey’s series

This series is funded by Curtis J Humphreys which occurs when the electrons migrate from a higher energy state to a lower one (nl = 6).

## Conclusion

The tutorial has shed light on the representation of the concept of the spectral series that can be observed from different perspectives at different stages of the atom spectrum of hydrogen. In the tutorial, it has been included that in order to calculate the emission of the spectrum, the formula that has the mathematical expression like $\mathrm{\frac{1}{\lambda}=RZ^{2}(\frac{1}{n_1^{2}} −\frac{1}{n_2^{2}})}$ is used. In this formula, the value of R is considered 1.09737 ✕ 10^{7} m⁻¹. Moreover, the tutorial has explained several different types of spectral series.

## FAQs

**Q1. What is a photon?**

Photons can be referred to as fundamental subatomic particles that are responsible for carrying electromagnetic force.

**Q2. Which atomic system is called the simplest in the universe?**

Hydrogen is considered the simplest atom as it consists of one electron and one proton and with that Hydrogen has its presence in three-fourths part of the universe.

**Q3. How many spectral lines are observed in the spectrum?**

Two types of spectral lines can be observed in the spectrum, such as emission lines and absorption lines. Emission lines occurs when the wavelength is emitted by the particles, whereas the occurrence of an absorption line happens when the wavelength is absorbed by the particles.

**Q4. How is calculate spectral lines done?**

The mathematical representation of the formula with the help of which the calculation of the spectral lines is possible is written as (n_{2} - n_{1}) (n_{2} - n_{1} + 1)/2. This particuler formula represents the possible numbers of spectral lines.

## References

### Journals

Du, C., Zhang, X. N., Sun, T. L., Du, M., Zheng, Q., & Wu, Z. L. (2021). Hydrogen-bond association-mediated dynamics and viscoelastic properties of tough supramolecular hydrogels. Macromolecules, 54(9), 4313-4325. Retrieved from: https://www.researchgate.net

McGuire, B. A., Loomis, R. A., Burkhardt, A. M., Lee, K. L. K., Shingledecker, C. N., Charnley, S. B., ... & McCarthy, M. C. (2021). Detection of two interstellar polycyclic aromatic hydrocarbons via spectral matched filtering. Science, 371(6535), 1265-1269. Retrieved from: https://arxiv.org/pdf/2103.09984

Quimby, R. M., De Cia, A., Gal-Yam, A., Leloudas, G., Lunnan, R., Perley, D. A., ... & Yaron, O. (2018). Spectra of hydrogen-poor superluminous supernovae from the Palomar Transient Factory. The Astrophysical Journal, 855(1), 2. Retrieved from: https://iopscience.iop.org/article/10.3847/1538-4357/aaac2f/pdf

### Websites

En.universaldenker, (2022). Rydberg Formula for Hydrogen. Retrieved from: https://en.universaldenker.org/formulas/743 [Retrieved on 17th June 2022]

Ucolick, (2022). Spectral Line Formation. Retrieved from: https://www.ucolick.org/~bolte/AY4_00/week2/spectral_line_formation.html [Retrieved on 17th June 2022]

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