Balmer series-chemistry learners

 The Balmer series

Introduction of the Balmer series

The first rank or the first position, first-class or the class first, are words alluring to everyone. Because the first is always the best. Similarly, something that happens for the first time drags everyone's attention. You might be confused about the repeated use of the word 'first'; yeah, you got the correct doubt. Today, we are discussing the first discovered series of the hydrogen spectrum. I hope you can guess it correctly. Okay, this is the Balmer series. And in this blog post, we discuss only the Balmer series of the hydrogen spectrum.

The Balmer series is the spectroscopic invention of the scientist Johann Jakob Balmer. It occupies second place among the six series of the hydrogen spectrum. You might think that; 

Why the first discovered series of the hydrogen spectrum is in the second place?

 Since all spectral emission lines in the Balmer series correspond to the electron transitions from top-level energy orbits greater than two to the principal quantum number n=2. And we all know that the classification of spectral series derives from the lower energy state of the electron during its transition. In the Balmer series, the lower energy state of the electron or the ground state is the second energy level. Consequently, it is in second place among the six hydrogen spectral series.

Additional reference:

A beautiful PowerPoint presentation the hydrogen spectral series

An infographic on the common names of the hydrogen emission spectrum

In this blog post, we will learn about what is Balmer series? And its history, the Balmer formula, and its significance in astronomy. So, without further delay, let us discuss the definition of the Balmer series.

It is a Balmer series image.
Balmer series diagram

What is the Balmer series?

The Balmer series is a hydrogen spectral series. The mathematician Johann Jakob Balmer discovered it in 1885. Not to mention, you are aware that it is the second series of the hydrogen spectrum. It signifies the lower energy state of the hydrogen electron for the Balmer series.

The hydrogen atoms present in the discharge tube absorb energy from the electric current that flows through it. It causes the excitation of the hydrogen electron from the ground state to one of the higher energy orbits with a quantum number equal to n≥3. After being unstable, the hydrogen electron jumps back to its initial lower energy position n=2 with the emission of photons of a definite wavelength. It gives spectral lines in the Balmer series.

The image shows the colored spectral emissions in the Balmer series of the hydrogen spectrum
The four colored spectral emissions in the Balmer series

And all the spectral emission lines in the Balmer series emit photons with wavelengths between 400-700 nm. It denotes that the Balmer series occurs in the visible region of the electromagnetic spectrum.

History of the Balmer series

Since the 1550s, in the smelting of ores, the flame color served as a qualitative application to identify the chemical substances. Because each chemical element imparts its characteristic color to the flame when heated. On heating, the atoms of the chemical substances absorb heat energy that causes the excitation of its electrons. And while returning to the lower energy state, they give off their excess energy in the form of light. It shows different colors in the flame when the wavelength of the emitted light radiation fall in the visible region.

This method helped find their chemical composition rather than the amount of substance present in the ores. But the intensity of light acquired in the process helps in their quantitative analysis.

In 1666, Sir Isaac Newton used this atomic emission phenomenon to study the different colors of sunlight. He used a prism to disperse the sunlight into individual wavelengths. Then Newton kept a screen to display the solar emission lines. To which he named it a spectrum.

Later, Joseph von Fraunhofer used a diffraction grating instead of a Newton prism for the dispersion of sunlight. He demonstrated the effectiveness of various slits such as a rectangular slit, single slit, and double slit for spectral emissions. Moreover, he observed some dark bands in the solar absorption spectrum with his diffraction grating technique. They were later named Fraunhofer lines.

Besides, Anders Jonas Ångström's experiments on solar spectral lines inspired Balmer to carry out the experiments on the hydrogen atomic spectrum. Angstrom studied the wavelengths of spectral lines in the solar spectrum and expressed them in units of 10-10 meters. And this measurement became a unit for atomic length named after him as Angstrom.

In 1885, Jakob Balmer discovered an empirical equation to calculate the wavelengths of hydrogen emission lines in the visible region of the hydrogen spectrum. And it is termed the Balmer formula.

Additional reference:

What is the history of the atomic emission spectra?

An infographic on the history of the Balmer series

Scientist life history

Johann Jakob Balmer was a Swiss mathematician. And he was born in Lausen, Switzerland, on 1 May 1825. He was the elder son of Elizabeth Rolle Balmer and Johann Jakob Balmer (his father's name was the same as his name).

From childhood, he had a good command of Mathematics subject. Balmer studied mathematics at the University of Karlsruhe and the University of Berlin. And at the University of Basel, he submitted his thesis on the cycloid in 1849. Balmer spent his entire life as a math teacher in Basel. And he also delivered his lectures at the University of Basel.

In 1885, he interpreted an empirical formula to calculate the wavelengths of the hydrogen emission lines in the visible region. In 1888, Rydberg generalized this Balmer formula to calculate the wavelengths of all spectral lines of the hydrogen spectrum. It laid the foundation to discover the other spectral series of the hydrogen spectrum. The other physicists, Lyman, Paschen, and Brackett, predicted the hydrogen spectral lines outside the visible region.

For his contributions to the scientific world, a spectral series of the hydrogen spectrum named as Balmer series. And his empirical formula and the constant h of his formula were popularly known as the Balmer formula and the Balmer constant.

In stellar classification, the Balmer jump is a valuable theory named after him. In addition to that, a crater on the moon was also named Balmer in his honor.

Overview of the Balmer series

Balmer is well renowned for his research on the hydrogen spectral series. The part of the hydrogen emission spectrum that corresponds to electron transitions from higher orbicular states n>2 to the energy level with principal quantum number n=2 is a series of spectral lines known as the Balmer series. And the Balmer series consists of a sequence of spectral emissions in both ultraviolet and visible regions of the electromagnetic spectrum. Please check out our engaging infographic on Overview of Balmer series.

With the suggestion of Eduard Hagenbach, he utilized Angstrom’s measurements on solar emissions to find a formula for the visible spectral lines of hydrogen. It was popularly known as the Balmer formula. And it computes the wavelengths of the hydrogen emission lines in the visible region.


The image shows the Balmer formula to calculate the wavelengths of visible hydrogen spectral lines.
The Balmer formula

Where,

λ is the wavelength of emitted spectral lines of hydrogen

h is a constant known as the Balmer constant

m is a principal quantum number that equals two

n is an integer provided n>m. It’s value can be 3,4,5,….,

The hydrogen spectrum has four colored spectral lines in the visible region called the hydrogen color spectrum. The wavelengths of these visible spectral lines lie between 400-700 nm. There are innumerable Balmer lines in the ultraviolet zone with wavelengths shorter than 400 nm. In the ultraviolet region, we observe an infinite continuum while approaching 364.506 nm, which is the series limit of the Balmer series.

The spectral lines with wavelengths shorter than 364.506 nm have not been observed yet in the Balmer series. Hence, this wavelength is the series limit for the Balmer series.

Additional reference:

A PowerPoint presentation on the hydrogen emission spectrum

An infographic explaining the Balmer series of the hydrogen spectrum

What do you mean by a series limit?

We all know the spectrum is an arrangement of wavelengths of emitted light radiations. All the spectral lines in a series have the same initial principal quantum number.

Series limit is the region between the starting line and the limiting line of the series. The starting line is the point at which the atomic line starts, and it will progress towards higher wavelengths. And at the limiting line, the series ends. The limiting line is the endpoint where no additional lines will occur in that series.

Even though the Balmer series occurs in two regions of the electromagnetic spectrum, we usually say the Balmer series is in the visible region. Why?

The Balmerseries of the hydrogen spectrum show spectral emissions in both visible and ultraviolet regions. But, in our discussions, we generally speak that the Balmer series is in the visible zone. The reason behind it is;

  • Due to the abundance of hydrogen in the universe, we commonly see Balmer series spectral lines in the celestial bodies. The majority of these spectral emission lines lie in the visible part of the hydrogen spectrum. The human eye detects them easily without much effort.
  • The spectral emissions in the ultraviolet region correspond to higher energy transitions, which have not yet been discovered completely.

Hence, due to the predominance importance of the visible part of the Balmer series over the ultraviolet region, we generally speak that the Balmer series occurs in the visible zone of the electromagnetic spectrum.

Additional reference:

An infographic on the comparative explanation of the visible and ultraviolet regions of the Balmer series.

 Hydrogen visible spectrum

In the visible zone, we observe four spectral lines at wavelengths 656nm, 486nm, 434nm, and 410nm correspond to electron transitions from energy levels such as 3 to 2, 4 to 2, 5 to 2, 6 to 2 giving characteristic red, aqua, blue and violet colored emissions in the hydrogen spectrum. This portion of the Balmer series is also known as the visible hydrogen spectrum.


The image represents the spectral emission of the Balmer series in the visible region.
Hydrogen visible spectrum

These transitions are also referred to sequentially by Greek letters. The electron transition from the third stationary orbit to the second is known as Hydrogen-alpha or H-α. And Hydrogen beta refers to the electron movement from the fourth main energy level to the second level. The hydrogen gamma spectral line is due to electron transference from the fifth stationary configuration to its early level. Finally, the hydrogen delta spectral line occurs by the electron transition from the sixth orbit to the ground state n=2.

This image is a table showing the details of the visible hydrogen spectrum.
Hydrogen visible spectrum table

Out of these four spectral emissions, we observe an intense spectral line during the electron movement from the third energy level to the second level. It is a bright red spectral line in the emission spectra of hydrogen or the ionization nebula.

The image shows the Orion nebula region in a milky way
The picture of Orion nebula

Indeed the most famous H II region is the Orion nebula. It is an interstellar matter consisting of ionized hydrogen atoms cloud that gives a reddish-pink colored visible hydrogen spectral emission line. The color variation is due to the combining effect of other electron transitions in the visible zone. 

At sufficient temperature, a significant number of hydrogen atoms absorb energy that corresponds to the energy difference between the third and second stationary levels. It results in the electron transition between these two static configurations with the emission of a spectral line having a longer wavelength at 656 nm in the hydrogen atomic spectrum. Therefore, it is the most intense spectral line in the hydrogen visible spectrum with a bright red color.

Which part of the electromagnetic spectrum can we see? And why?

The electromagnetic spectrum is the patterned arrangement of all kinds of light radiations in the increasing (or decreasing) order of their wavelengths and frequencies. From them, the human eye can see visible light radiations with wavelengths ranging from 380nm to 700 nm. Only these wavelengths can stimulate the human eye's retina during light observation.

The visible part of the light consists of seven-colored radiations of the sunlight. They are violet, indigo, blue, green, yellow, orange, and red.

The wavelength variations of these seven-colored radiations are below;

The image shows a table with wavelengths data of visible light radiations
The wavelengths data of light in the visible region

Additional reference:

UV Balmer spectrum

The electron transitions from the principal quantum number n>6 to the Balmer series ground state n=2 emit spectral lines in the ultraviolet region of the electromagnetic spectrum. Further, Balmer colleagues Wilhelm Vogel and William Huggins confirmed these spectral emissions in the white stars. Moreover, these electron transitions are also symbolized sequentially with Greek letters shown in the following table. 

It shows the image of the ultraviolet Balmer spectrum.
The Ultraviolet Balmer Spectrum

The spectral line formed due to the electron transition from the static configuration n=7 to the normal state n=2 is known as hydrogen epsilon. The hydrogen zeta emission line is due to the electron transition from top energy level n=8 to the ground state n=2 at a wavelength of about 389 nm. Similarly, the electron movement from n=9 to n=2 results in a spectral line named hydrogen eta. Finally, the spectral emission that results from n=∞ to the Balmer series ground state n=2 at 364.5 nm is the series limit of the Balmer series.

This image is a table showing the details of the UV Balmer series
The UV Balmer series table

From the spectral studies, Balmer found that a single wavelength has relation to every spectral line in the visible region of the hydrogen spectrum. And that wavelength is 364.5 nm. Hence, it is also known as the Balmer break.

Why does the Balmer series of the hydrogen spectrum occur in two regions, namely ultraviolet and visible but all the other hydrogen spectral series occur in a single zone of the electromagnetic spectrum?

The hydrogen spectrum consists of six spectral series in the ultraviolet, visible, and infrared regions. Except for the Balmer series, the other series show spectral emissions in a single zone of the electromagnetic spectrum. But the Balmer series show spectral emissions in two zones such as ultraviolet and visible regions of the electromagnetic spectrum. Before discussing its reason, let us first discuss the Balmer series briefly.

In 1885, the scientist Johann Jakob Balmer discovered a series of hydrogen spectral lines in the visible region. Later his colleagues found a few more spectral emissions in the ultraviolet region. These spectral emission lines occur during the electron transition from the top energy levels with principal quantum number n>2 to the second stationary orbit of the hydrogen spectrum. Hence, the series of all the spectral emissions that occur with the ground state quantum number n=2 during the electron transitions is known as the Balmer series.

The electron transitions from higher energy orbits to lower stationary states proceed with the emission of the photons of definite wavelengths.

If the wavelengths of the emitted light radiations lie between 400-and 700 nm, then the spectral lines occur in the visible region. Similarly, the spectral emission lines with wavelengths below 400 nm give spectral lines in the ultraviolet zone.

According to the quantum theory of radiations, the energy of a photon varies inversely with the wavelength of the emitted light radiations.

If the energy gap between the two successive stationary orbits is high, then the emitted photon gives a spectral line at a shorter wavelength. So, the electron transitions from the highest energy orbits, such as n>6, give spectral emissions in the ultraviolet region. Consequently, the electron transitions till n=6 give spectral emissions in the visible part.

It is the peculiar condition of the Balmer series giving spectral lines in two different regions of the electromagnetic spectrum. Whereas in the remaining five hydrogen spectral series, the higher electron transitions give spectral emission lines in the same part of the electromagnetic spectrum as the lower transitions.

Additional reference:

Why does the Lyman series lie in the ultraviolet region?

Why Balmer series is visible?

Balmer break

In the stellar continuum spectrum, the Balmer break is the intensity difference on either side of the Balmer series limit nearly at 364.5 nm.

It occurs due to the bound-free absorption of hydrogen electrons at the ground state n=2 resulting in their complete ionization.

The bound free absorption in the Balmer series results in the continuum absorption at wavelengths shorter than 364.5 nm. It is otherwise called Balmer discontinuity. The other hydrogen spectral series show continuum discontinuity at wavelengths shorter than their series limit. But, the Balmer break is observed apparently in the ultraviolet region of the hydrogen spectrum.

The temperature and density of the absorption region affect the strength of continuum absorption or the size of the Balmer break.

In cooler stellar regions, the density most strongly affects the continuum strength. It helps to classify stars based on their surface gravity. However, in hotter stars, the temperature affects the discontinuity strength immensely more than the density.

Balmer series formula

From the history of the Balmer series, we can understand that physicists' experiments on the atomic emission spectrum started in the 1550s. But they lacked an empirical formula to imagine the wavelengths of spectral lines of an element. In 1885, the Balmer equation was the first empirical formula discovered to estimate the wavelengths of spectral emissions in the hydrogen spectrum. The Balmer equation was given by the mathematician Johann Jakob Balmer.

His great benefaction to astronomy and chemistry was discovering an empirical formula to estimate the spectral lines in the visible region of the hydrogen spectrum in 1885. It calculated the spectral emissions wavelengths when the electron alters from a stationary configuration higher than two to an orbicular state that is equal to n=2. To do so, he took Angstrom's atomic size calculations into account. According to Angstrom, the radius of an atom is equal to 10-10 meters. 

So, the Balmer formula for the spectral emissions in the Balmer series of the hydrogen line spectrum is below;

It shows the Balmer series formula
The Balmer series formula

In the above formula, h is the Balmer constant, and its value is 364.506 nm. This Balmer constant value interprets the series limit of the Balmer series. During his spectral studies, Balmer found that a single wavelength has a relationship with all the spectral emission lines in the visible region of the Balmer series. And that wavelength is 364.506 nm. In addition to that, there are no more spectral lines in the Balmer series with wavelengths shorter than this figure. So, the wavelength 364.506 nm is the series limit of the Balmer series. In simple terms, the Balmer series ends at this point.

m is an integer. And m=2. It implies the ground state of the electron in the Balmer series for the electron transitions is two.

n is an integer. And its value must be greater than m. The value of n starts with 3 and ends at infinity.

According to the Balmer equation, the wavelengths of spectral lines are obtained when any integer value higher than two was squared and then divided by itself squared minus four. And the achieved value should be multiplied by the Balmer constant value of 364.506 nm.

The wavelengths of hydrogen spectral lines gave accurate results for spectral emissions in the visible region. The Balmer equation gives precise results for the four visible hydrogen spectral lines. But, when the value of m is greater than 6, the electron transition gives spectral emission in the ultraviolet region. The Balmer equation calculations are slightly inaccurate for the spectral emissions of the ultraviolet region.

Meanwhile, Hagenbach informed Balmer that Angstrom got a hydrogen spectral line at 397 nm for electron transitions from n=7 to the second stationary state. It paved the way for the modification of the Balmer equation.

Additional reference:

What is the Rydberg-Ritz combination principle?

What are the six series of the hydrogen spectrum?

Rydberg formula- a generalization to Balmer equation

In 1888, the physicist Johannes Rydberg generalized the Balmer formula with the necessary modifications. The Rydberg formula helps to calculate the wavelengths of all spectral lines that occur in the hydrogen spectrum with the help of an empirical fitting parameter known as the Rydberg constant.

The Rydberg equation involves a simple reciprocal mathematical rearrangement necessary to get accurate results for calculating the wavelengths of hydrogen spectral lines in the Balmer series along with all the other series of the hydrogen spectrum.

The Rydberg equation to calculate the wavelengths of Balmer series spectral lines is below;

It shows the Rydberg formula to calculate the wavelengths of spectral lines in the Balmer series.
The Rydberg equation for Balmer series

Where,

RH is a Rydberg constant for the hydrogen atom and its value equal to 10973731.57 m-1

n is an non-negative positive integer with value starts from 3 and proceeds towards infinity.

λ is the wavelength of emitted spectral lines in the hydrogen spectrum

What is the Rydberg constant of a hydrogen atom?

The Rydberg constant of the hydrogen atom is a constant quantity that should be used with every spectral line of the hydrogen spectrum. The above formula shows it. The symbol RH denotes it. The following formula shows the relationship between the Balmer constant (h) and the Rydberg constant of the hydrogen atom.

The image is a formula that shows the relationship between the Balmer constant (h) and the Rydberg constant of the hydrogen atom.
The relationship between the Balmer constant and the Rydberg constant of the hydrogen atom

For infinitely heavy hydrogen nucleus, it implies;

It shows a calculation for the Rydberg constant value.
The calculation of the Rydberg constant value

As a final note, the Rydberg constant is a constant number. And it is the ratio of two square to Balmer constant h. It helps to calculate the wavelengths of all hydrogen spectral lines that occur in the hydrogen emission spectrum.

The Rydberg formula used generally to calculate the wavelengths of all spectral lines in the hydrogen spectrum is

It shows the Rydberg formula for all the spectral lines of the hydrogen spectrum.
The Rydberg formula

Where,

λ = wavelength of the emitted electromagnetic radiation

n1 = lower energy level of the electron transition

n2 = higher energy level of the electron transition

RH= Rydberg constant

Hydrogen- alpha

It is the first line that occurs in the Balmer series of the hydrogen spectrum. Hence, the initial Greek symbol α denotes it. Jointly, we call it the hydrogen alpha spectral line. And in rare circumstances, we also call it the Balmer alpha line that indicates the Balmer series of the hydrogen spectrum.

It is a deep red colored spectral line that occurs in the visible region at 656.28 nm in air. And it is the brightest hydrogen spectral line in the hydrogen visible spectrum. The electron transition from the third stationary orbit to the second energy level of the hydrogen atom gives this hydrogen-alpha spectral line. Due to the small energy difference between these two second and third stationary orbits, hydrogen-alpha spectral lines occur at a longer wavelength with the least energy emission in the Balmer series. So, we can see it at the end of the visible region of the electromagnetic spectrum.

It shows the hydrogen-alpha emission line in the Balmer series of the hydrogen spectrum.
Hydrogen alpha emission in the Balmer series

It is the most intense spectral emission in the visible region of the hydrogen spectrum. It indicates that it is the most abundant spectral emission of the hydrogen spectrum. At sufficient temperature, a large number of the hydrogen atoms prefer to transit between the third and second energy levels of the hydrogen atoms. It enhances the number of transitions between these two stationary orbits. It, in turn, increases the number of photons emissions. But, it does not impact the number of spectral lines at 656.28 nm. Since the values of principal quantum numbers for the electron transition are unchanged, we get only one red-colored bright spectral line. To conclude, the intensity of the spectral line is directly proportional to the number of atoms participating in the electron transition.

The image shows the electron transition corresponding to the hydrogen alpha emission line.
The hydrogen alpha transition in the Balmer series of the hydrogen spectrum

The ionization energy of one hydrogen atom is 13.6 eV. And the energy difference between the n=1 to n=3 is 12.1 eV. So, a large number of hydrogen atoms prefer to ionize before their transition between the third and first stationary levels of the hydrogen atom. It favors the ejection of electrons from the hydrogen atoms to produce H+ ions. Again, the formation of new hydrogen atoms takes place by the combination reaction of the electron and the proton. The majority of newly formed hydrogen atoms proceed with n=3 to n=2 electron transition after recombination. Hence, it will emit the most intense bright red colored hydrogen alpha spectral line. It intimates that the hydrogen alpha emissions occur when the hydrogen gas ionization occurs. Therefore, the red spectral emission lines help astronomers trace the ionized electron clouds in the astronomical bodies.

Additional reference:

Why does the hydrogen alpha spectral line seem doublet with a high-resolution spectrometer?

What is the importance of Lyman-alpha line?

Importance of the hydrogen alpha line:

As mentioned earlier, hydrogen-alpha emissions indicate ionized hydrogen atoms clouds and the emission nebulae and help astronomers identify them.

Due to the hydrogen abundance in the universe, hydrogen-alpha emissions help to observe the sun’s atmosphere features, including solar prominences and chromosphere.

Hydrogen alpha filter

The hydrogen-alpha filter is an optical filter used to filter out the hydrogen-alpha wavelength by stopping all the unnecessary wavelengths of sunlight.

The hydrogen-alpha filters are dichroic interference filters made with multiple vacuum deposited layers. It relies on the interference of internal light reflections that reflect between that surfaces.

In short, the hydrogen alpha filters transmit the narrow bandwidth of light radiations by focusing on hydrogen alpha wavelengths.

They are used in astrophotography and to reduce light pollution in solar observations.

Additional reference:

What is the hydrogen spectral series?

What is the Lyman alpha?

Fine structures of the Balmer series spectral lines:

The electron transitions in the hydrogen atom result in spectral lines in the atomic spectrum of hydrogen. We observe a single spectral line corresponding to a single electron transition with spectrometers. But, the high-resolution spectrometers show the splitting of the main spectral line into two or more components with a slight variation in the wavelengths. These diverged spectral lines are known as fine structures of the main spectral line.

Hydrogen is a simple element with a single electron in it. In the presence of a magnetic field, we observe closely spaced spectral lines doublet for the hydrogen spectral lines. These are the hydrogen fine structures.

The hydrogen fine spectrum is the dissociation of the hydrogen main spectral line into its constituent spectral emission lines.

The hydrogen spectrum consists of six series of spectral lines. They occur in the visible, ultraviolet, and infrared regions of the electromagnetic spectrum. In this blog article, we will discuss the spectral splitting of the Balmer series.

In the Balmer series, we all know red, aqua, blue, and violet-colored spectral emission lines in the visible region. Out of them, the red-colored spectral line at 656.28 nm shows spectral splitting in the presence of the magnetic field. The high-resolution spectrometer shows a pair of closely spaced spectral lines for the hydrogen alpha line. They are hydrogen-alpha fine structures.

It shows the fine structures of the hydrogen-alpha emission line.
The hydrogen alpha fine structures

According to atomic structure theories, an atom consists of a hefty nucleus at the center with revolving electrons in discrete energy levels. The revolution of electrons around the nucleus in fixed orbits generates a magnetic field in the atom.

The interaction of the spinning electron with the magnetic field generated by the electron's orbital motion around the nucleus causes the splitting of spectral lines in the atom.

 The hydrogen-alpha emission occurs due to the electron transition from the higher energy orbit n=3 to the lower energy state n=2. And the emitted light radiation at 656.28 nm gives the alpha spectral line in the hydrogen spectrum. The splitting of the spectral line takes place when the emitted light radiation is affected by the atom's magnetic field. The powerful spectrometer detects it.

Additional reference:

What do you mean by the hydrogen spectral line?

Applications of the Balmer series

  1. The study of the Balmer series is most useful in astronomy. As many stellar objects generally show the Balmer series spectral lines. Due to the plethora of hydrogen in the universe, these are the most intense spectral lines compared with the other element's spectral lines.
  2. It plays a significant role in the spectral classification of stars like surface gravity and composition. Based on its predominance, the relative strength of these spectral lines determines the star's surface temperature.
  3. It helps to find out the radial velocities of the celestial bodies due to the Doppler shifting of the Balmer series.
  4. The Balmer series helps to detect binary stars, exoplanets, star clusters, galaxy clusters, etc. In addition to that, its close analysis helps to identify unknown astronomical bodies.
  5. It also estimates the redshifts of galaxies or quasars.
  6. The occurrence of emission or absorption lines of the Balmer series depends on the nature of the astronomical object. In the stars with a surface temperature of about 10,000 kelvins, the Balmer series absorption lines are seen. But, in the spectra of irregular galaxies, H II regions, the Balmer lines are the spectral emission lines.

Maximum and minimum wavelengths of Balmer series:

The electron transitions from n ≥3 to n=2 result in the emergence of a sequence of spectral lines in the Balmer series of the hydrogen spectrum. Consequently, the n1 and n2 values of the Balmer series vary from 2 to infinity.

The maximum wavelength for the Balmer series is 656 nm, and the minimum wavelength is 364.5 nm. Hence, the limits of the Balmer series are 656 nm and 364.5 nm.

It shows the computation method of wavelengths for the spectral lines in the Balmer series.
The maximum and minimum wavelengths of spectral lines in the Balmer series

Additional reference:


 Position of the Balmer series in the hydrogen spectrum

The hydrogen atomic spectrum consists of a sequence of spectral lines arranged in the decreasing order of their wavelengths and the increasing order of their frequencies. And the hydrogen spectrum consists of six series named after the scientists who discovered them. The six series of the hydrogen spectrum are;

  • Lyman series
  • Balmer series
  • Paschen series
  • Brackett series
  • Pfund series
  • Humphreys series

On observing the sequential order of the hydrogen spectral series, we understand that the Balmer series is in second place.

Here is a trick to remember all the six series of the hydrogen spectrum without much effort.

The order of hydrogen spectral classification intimates the electron's ground state during the electron transition. In the Balmer series, the principal quantum number value for the ground state of the electron is n=2. Hence, it is in second place in the hydrogen spectral series.

In the same way, the Lyman series having electron's ground state principal quantum number n=1 is in the first place.

This image shows the six series of the hydrogen spectrum
The six series of the hydrogen spectrum

Final thoughts

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