Lyman-alpha line-chemistry learners

 Lyman alpha line of the hydrogen spectrum

Lyman-alpha is a hydrogen spectral line that generally occurs in quasar spectra. It has vast significance in astronomy as most intergalactic spaces with neutral hydrogen clouds show Lyman-alpha forest with a bunch of Lyman-alpha absorption lines. It was named after the Harvard physicist Theodore Lyman.

The Lyman-alpha spectral line results due to electron transition from the first stationary ground level of the atom to its immediate next higher orbicular configuration n=2 in the hydrogen spectrum. The Greek letter α denotes it, and its symbolization is Ly-α. In the same way, the Lyman series of the hydrogen spectrum initiates by the Lyman-alpha line.

It lies in the vacuum-ultraviolet region. It is characterized by a strong absorption in the air. Hence, satellite-borne instruments are used to study the Lyman-alpha astronomy.

The Lyman-alpha line in astronomy

How was the hydrogen spectrum obtained?

We are talking that Lyman-alpha occurs in the hydrogen spectrum. But, do you know? What is the hydrogen spectrum? How was it obtained?

The hydrogen spectrum is the arrangement of electromagnetic light radiations emitted or absorbed by the hydrogen atom in decreasing order of their wavelengths and increasing sequence of their frequencies. Observation of absorbed light radiations by the hydrogen atoms gives the hydrogen absorption spectrum. Conversely, the arrangement of emitted light radiations of the hydrogen atom shows the hydrogen emission spectrum.

Additional reference:

A beautiful infographic on Lyman-alpha line 

What is the hydrogen spectrum?

A PowerPoint presentation on the hydrogen spectrum

Find the detailed differences between the hydrogen absorption and emission spectra:

When the energy of the supplied light radiation is greater or equal to the energy difference between the static orbicular electron paths of the hydrogen atom as proposed by Bohr, the absorption of the photon (the packet of light energy) takes place. Analyzing the transmitted light radiation after passing through the hydrogen gas gives the hydrogen spectrum. To acquire it, we pass the transmitted light beam through the prism and then allow it to fall on the photographic plate. The analyzed result of the transmitted light beam shows the sequential wavelength arrangement of the absorbed photons by the hydrogen atom, known as the hydrogen absorption spectrum.

The hydrogen spectrum experimental setup

Likewise, if we proceed further and analyze the emission lines formed by the electron transitions, it gives the hydrogen emission spectrum. The process is pretty simple. The hydrogen atom on absorbing photon commences the electron transition between the corresponding energy levels. And it causes the release of electromagnetic radiation of definite frequency when the electron returns to its original position. As mentioned earlier, the emitted light radiation is allowed to pass through the prism and captured by the spectroscope to generate its spectrum. It is known as the hydrogen emission spectrum.

In both cases, a sample of the hydrogen gas is taken in the discharge tube at low pressure and high voltage conditions that facilitate the electron processes without much hindrance.

Have a look at the infographic on experimental setup for the hydrogen spectrum

It is all about the procedure to obtain the hydrogen spectrum. Let us discuss a brief on the series of the hydrogen spectrum.

Additional reference:

An infographic on the types of the hydrogen spectrum

The hydrogen spectrum consists of six series. They are;

1. Lyman series
2. Balmer series
3. Paschen series
4. Brackett series
5. Pfund series
6. Humphreys series

A trick to remember the hydrogen spectral series

The classification is based on the initial stable state of the electron allowed for its motion around the nucleus, known as the ground state.

Our topic of discussion relates to the Lyman series of the hydrogen spectrum, where the Lyman alpha spectral line is observed.

Additional reference:

What are the six series of the hydrogen spectrum?

A PowerPoint presentation on series of the hydrogen spectrum

A brief overview of the Lyman series:

The Lyman series is the sequence of discrete spectral lines observed during the electron movement from the top energetic stationary orbits such as n≥2 to lower energy ground state n=1, where n is the principal quantum number. It designates the energy levels of the atom. To calculate the wavelengths of acquired photons, we employ an empirical formula as shown below;

Lyman series formula

The electron oscillation between n=2 to n=1 gives the Lyman-alpha emission, and the electron transference from n=3 to n=1 shows the Lyman-beta line. In the same way, the Lyman-gamma line occurs during the electron transference between n=4 to n=1, and so on. The names of all these spectral lines involve a Greek letter coupled with its inventor name Theodore Lyman as an honorary contribution for his tireless scientific work from 1906 to 1914.

Lyman series table

The initial principal quantum number n1value for the Lyman series is 1. And the final quantum number n2 shows a wide range variation in values from 2 to ∞ that results in a bunch of spectral lines in the Lyman series. 

If you observe their arrangement pattern, there are an innumerable spectral lines showing dense spectral bands with narrow spectral lines packed as we move towards infinite states. Hence, we can see a few initial widespread emission lines and the last line distinctly in the Lyman series. These infinite spectral occurrences intimate the direct and intermediate pathways followed by the electron to reach its destination correlating with the energy fluctuations that happen to take place during the electron transition. Comparatively, the discontinuous spectral appearances confirm the existence of quantized electron orbits that accounts for atomic stability.

The wavelength data indicates that the longest and shortest wavelengths of the Lyman series are 121 nm and 91 nm, respectively. The below table gives detailed wavelength data for the Lyman series spectral emission lines.

The wavelength table for the Lyman series

The wavelength table shows the range of the Lyman series varies approximately between 90-120 nm. Since all the spectral lines wavelengths of the Lyman series lie below 400 nm. Hence, it clarifies their presence in the ultraviolet region. 

Therefore this ultraviolet spectral pattern is invisible to a normal human eye, and special spectrographic techniques are essential to identify them accurately. 

Additional reference:

Why does the Lyman series lie in the ultraviolet region?

An infographic on the Lyman series of the hydrogen spectrum

Timeline for the Lyman series:

In the early 1550s, in the smelting of ores method, the flame imparted characteristic colored emissions of metal played a vital role in quantitative as well as the quantitative analysis of ores. But, Newton’s optics experiments on sunlight from 1666 to 1672 effectuated the trends in atomic emission spectroscopy. It was instigated with the first spectrometer invention by Hyde Wollaston in 1802.

Equally, Fraunhofer diffraction grating techniques and the Pickering-Fowler series stood milestones in spectral studies.

Still, some flimsiness remained in spectral observations. And it is fulfilled by Balmer with his empirical formula to calculate the wavelengths of the visible emission lines. It was further generalized by Rydberg in 1888 to apply to all the spectral series of the hydrogen spectrum. This modification accelerated the origination of hydrogen spectral lines later. The Lyman series discovery even happed in the same way.

Theodore Lyman, who researched the ultraviolet spectrum of the electrically excited hydrogen atom, discovered the first line of this series named Lyman-alpha in 1906. With time, he found the other emission lines of the hydrogen spectrum in the ultraviolet region until 1914.

 In 1913 Neil Bohr’s atomic model elucidated the theoretical meaning of the Rydberg formula. And the electronic arrangement of the atom gave a clear picture of the spectral emission traits of the hydrogen atom.

Additional reference:

What are the four postulates of Bohr's atomic model?

An infographic on the Bohr's atomic model

Scientist life history:

The U.S. Physicist and spectroscopist Theodore Lyman IV was born on November 23, 1874, in Massachusetts, Boston. He completed his Ph.D. from Harvard University in physics and rendered his service as a Physics professor at Harvard University.

He researched light radiations of shorter wavelengths, particularly ultraviolet radiations and their properties. It made him discover the first line in the ultraviolet region of the Lyman series in 1906. By extending his hydrogen spectrum studies, he found the rest of the lines in the Lyman series from 1906 to 1914.

In addition to that, he studied the diffraction gratings phenomenon. With his contributions to physics, he was awarded the Franklin Institute's Elliott Cresson Medal in 1931.

What is the Lyman-alpha line?

It is the first spectral line of the hydrogen spectrum. The valence electron of the neutral hydrogen gas atom, while moving from the lowest stationary orbit with principal quantum number value n=1 to its immediate next energy level on absorbing energy, gives this Lyman-alpha spectral line in the ultraviolet region of the electromagnetic spectrum.

The hydrogen electron has -13.6 eV energy in the first stationary orbit. When it is in the second orbit, its energy is -3.4 eV. So, the difference in energy between the first and second static levels of the hydrogen atom is 10.2 eV. Therefore, the Lyman-alpha transition requires 10.2 eV energy to occur. 

The formula to calculate the energy difference between two energy levels

ΔE= energy difference between the two electron transition states

E₁ = Energy of the first main level

E₂ = Energy of the second main level

The energy gap calculation for Lyman-alpha

It is the lowest energetic transition of the Lyman series due to the small energy gap between the first and second orbicular configurations. Hence, the Lyman-alpha spectral line occurs at the longest wavelength of 121.5 nm. And it has the smallest frequency of 2.47X10¹⁵ Hz.

An interesting PowerPoint presentation of Lyman-alpha line 💛💛💛, posted on May 21.

The Lyman-alpha transition has two specificities. One is that it occurs at the lowest energy than the other electron transition of the Lyman series. And the second is that it occurs at the longest wavelength than the remaining spectral lines of the Lyman series.

It reminds us of the inverse proportional relationship between the energy and wavelength of light radiation.

The relationship between the energy and the wavelength of the light radiation

The Rydberg formula derived for the Lyman series is used to calculate the wavelength of the Lyman-alpha spectral line.

Wavelength calculation for the Lyman-alpha line

Similarly, the frequency of the Lyman-alpha spectral line is calculated from the following equation.

The formula showing relationship between the frequency and wavelength of the light radiation

Where,

ϒ = frequency of the light radiation

c = velocity of light in vacuum

λ = wavelength of the light

The frequency calculation for the Lyman-alpha line

The hydrogen spectrum reveals that it is the most intense spectral emission line in its ultraviolet region. This states it is the most abundant hydrogen spectral line in the Lyman series.

At suitable temperature conditions, the number of hydrogen atoms participating in the Lyman-alpha transition is more. And it enhances the photon emissions that influence the intensity of the Lyman-alpha spectral line.

But, an important thing to remember here is that the intensity of the spectral line does not impact the number of Lyman-alpha spectral lines appearing in the hydrogen spectrum since its transition states remain unchanged. Hence, we observe a thick single Lyman-alpha line at the extreme right end of the hydrogen spectrum.

Frequency variation of the hydrogen spectral lines

The ultraviolet radiations with wavelengths 100-200 nm are in the vacuum ultraviolet region. The Lyman-alpha radiation with 121.5 nm lies in the vacuum ultraviolet region. Moreover, it shows strong absorption by the air. And it helps in Ozone formation. In the upper earth's atmosphere, the oxygen molecules absorb Lyman-alpha emissions of sunrays. And it dissociates the oxygen molecules into their atoms. Later, the oxygen atoms combine with the undissociated oxygen molecules to form an Ozone. In this way, Lyman-alpha emissions help save the earth from harmful radiations by involving in the Ozone formation.

An interesting visual representation of Ozone formation posted on Jan 28, Instagram 

The formation of Ozone in the earth's atmosphere

Strong absorption by the air is the characteristic property of the Lyman-alpha spectral line. So, vacuumed spectroscopic equipment is essential in laboratory for Lyman-alpha observations. For this reason, the Lyman-alpha involved experiments done in satellite-borne instruments, except when observing the extremely distant sources whose redshifts allow the Lyman-alpha line penetrations into the earth's atmosphere. Therefore, the Lyman-alpha radiations can redshift from faraway celestial objects on to earth's crust.

Additional reference:

An infographic on unknown facts of Lyman-alpha line

Why does the line spectrum of hydrogen lines become closer as the frequency increases?

What is spectrum?

What is the importance of the Lyman-alpha line?

The quasars serve as high energetic photon emitters source. The light radiations emitted from quasars travel through the neutral gaseous clouds. The hydrogen atoms of gas clouds absorb photons having wavelengths matching the Lyman-alpha line. Hence, the spectra of quasars or distant galaxies show the Lyman-alpha absorption line.

The emitted quasar photons proceed in the space. While they travel through an intergalactic medium, the valence electron in the lowest energy state n=1 of the hydrogen atom absorbs a photon having a wavelength of 121.5 nm. The remaining unabsorbed quasar photons continue their journey in space. 

The photon absorbed by the hydrogen atom induces the electron transition between the first and second stationary orbits. And the unstable excited hydrogen electron then returns to its original position with the emission of light radiation at 121.5 nm. It shows the Lyman-alpha spectral emission line in the spectrum.

Lyman-alpha spectral transition on absorption of quasar photon

The energy required to bring about the Lyman-alpha transition is dependent on the energy gap between the first and second static configurations of the hydrogen atom. So, a photon with a wavelength of 121.5 nm is absorbed or emitted by the hydrogen atom to trigger the Lyman-alpha electron transition.

Both absorption and emission of quasar photons occur concurrently in the universe due to the abundance of neutral hydrogen gas clouds and the quasars.

When there are a lot of neutral hydrogen atoms present in the gas clouds, more and more quasar photon absorptions take place. Hence, in such cases, the plot of the intensity of light to its wavelength shows a dip at 121.5 nm that confirms huge Lyman-alpha absorptions. This graph indicates the amount of light absorbed varies directly with the probability of photon absorption and the number of hydrogen atoms along its path.

The wavelength of the quasar photon is shorter than 121.5 nm at the beginning. But, when it travels through space, its wavelength increases with the decrease in energy, and it shows redshifting. The neutral hydrogen atoms absorb an available number of light radiations with 121.5 nm wavelength approaching them. And the remaining photons with varying redshifts suffer energy loss in their journey while reaching the observer on the earth. Consequently, for distant quasars, the plot of light intensity vs. wavelength shows more than one dip or toughs in the path of quasar photons to the earth’s surface. The careful observation of the absorption map thus indicates the regions of intervening hydrogen gas clouds between the quasar and the observer.

The absorption map does not show any dips in case of no intervening hydrogen gas clouds. But, it is a hypothetical assumption only.

As a final note, the Lyman-alpha spectral studies help identify the presence of neutral hydrogen atoms in the universe. And it contributes to understanding the properties of celestial matter and its distribution, like hot dark matter.

It helps to calculate the cosmological constant by comparing the angular and radial lengths of the astronomical object at its redshift.

Additional reference:

What are the differences between the Lyman alpha and hydrogen alpha fine structures?

An infographic explains the differentiation of the Lyman-alpha and hydrogen alpha.

How is the Lyman-alpha line split due to fine structure?

The Lyman-alpha spectral line observation with an ordinary spectroscope showed a single spectral line in the hydrogen spectrum. But, with the advent of high-resolution spectroscopes, the Lyman-alpha fine structures were revealed. The spectral line splitting into fine structures disclosed the coupling of spin and orbital angular momenta of the spinning hydrogen electron.

The interaction of the magnetic field produced by the orbiting electron with the quantum mechanical spin gives the Lyman-alpha fine structures. The spin angular momentum of the hydrogen electron while interacting with its orbital angular momentum gives a resultant magnetic field. This effective magnetic field is known as electron spin-orbital angular momentum.

This relativistic interaction of the rotating electron spin with its orbital angular momentum splits the electron’s principal energy levels into unequal sub-energy states. Due to different transitional energies of energy sub-shells, more electron transitions occur, giving extra spectral emission lines named fine structures.

Hydrogen spectral line splitting due to spin-orbit coupling

Therefore, the Lyman-alpha spectral line splits to give a pair of spectral lines with a slight variation in their wavelengths due to the spin-orbit interaction. Consequently, the Lyman-alpha doublet consists of closely spaced two spectral emission lines at wavelengths of about 121.5668 nm and 121.5674 nm. And they are symbolized as Ly-α3/2 and Ly-α1/2 having j values 3/2 and 1/2, where j is the total angular momentum of the electron.

The figure shows a longer arrow for j=3/2 during the transition from 1S-orbit to 2P-orbit. It indicates a large energy gap between the two stationary sub-shells for Ly-α3/2 as compared with Ly-α1/2. It realizes Ly-α3/2 is high energy transition than Ly-α1/2. Hence, Ly-α3/2 spectral emission occurs at a slightly shorter wavelength than Ly-α1/2. From this conclusion, we can remind of the quantum theory of radiation for the inversely proportional relationship between the energy of the photon and the wavelengths of emitted light radiation.

Lyman-alpha fine structure

In case of Lyman-alpha emission, the hydrogen electron transit from 1S-orbit to 2P-orbit gives a spectral line doublet in the presence of the magnetic field. The electron motion is associated with the orbital quantum number (l) and the spin quantum number (s). Hence, the total angular moment quantum number (j) can be expressed as below;

Total angular momentum quantum number formula

When the electron is in 1S-orbit, its spin quantum number values are +1/2 and -1/2 depending upon the direction of the magnetic moment. And the angular momentum quantum number value for S-orbit is zero. So, the total angular momentum quantum number (j) for the 1S-orbit electron is ±1/2.

Total angular momentum quantum number for 1s-electron

Due to the absence of spin-orbit coupling in 1S-orbit, splitting does not take place in electron energy levels. So, the 1S-orbit has a single energy level.

In 2P-orbit, the spin-orbit interaction breaks the main energy level into its components. So, we observe two sub-energy levels for the electron in the 2P-orbit. The spin angular momentum quantum number values for the electron are +1/2 and -1/2. Additionally, the orbital angular momentum quantum number value for P-subshell is 1. The total angular momentum quantum number values are 1/2 and 3/2.

The total angular momentum quantum number for 2p-electron

The hydrogen electron transition from 1S-orbit to 2P-orbit gives spectral lines doublet as it involves the two 2P-orbit energy sub-states in the electron transition.

Additional reference:

An infographic on Lyman-alpha fine structures

What is spin-orbit coupling?

What do you know about the fine structures of a hydrogen atom?

Lyman-alpha forest:

Lyman-alpha forest is a series of absorption lines observed in the spectra of distant quasars and galaxies due to Lyman-alpha electron transitions of the neutral hydrogen atom of the intergalactic gas clouds. The journey of emitted photons of the quasars to the earth’s crust with different redshifts through the intervening intergalactic gas clouds containing neutral hydrogen atoms shows multiple Lyman-alpha absorption lines in astronomical spectroscopy.

An observation of a quasar named 4C 05.34 by astronomer Roger Lynds guided him to discover the Lyman-alpha forest in 1970. He noticed an unusually large number of absorption lines in the mentioned quasar spectrum. And he suggested most of those absorption lines were of the same Lyman-alpha transition.

Subsequent observations of John Bahcall and Samuel Goldsmith on afore stated quasar had confirmed the presence of unusual absorption lines without specifying their origin. Additionally, the high-redshifted quasars spectra showed the same system of narrow absorption lines.

Jan Oort argued that these unusual absorption lines were shown due to the absorptions of intergalactic gas clouds in superclusters.

When the galaxy or quasar light travels through the intergalactic gas clouds, the neutral hydrogen atoms absorb photons to exhibit the Lyman-alpha absorption lines in the quasar spectra.

The wide range of wavelengths shown for the absorption lines designate the neutral hydrogen gas clouds at different degrees of redshift depending upon their distance from the earth. The varying positions of absorption lines in the quasar spectrum specify the characteristic positions of gas clouds.

The higher number of absorption lines in the Lyman-alpha forest specifies that the observed quasar is at a higher redshift. When it reaches the redshift of about 6, the Gunn-Peterson trough is observed. It is the end of the reionization of the universe.

Uses of the Lyman alpha forest:

The Lyman alpha forest observations assist in investigating the intergalactic medium. In addition to it, some other uses of it are;

• It helps determine the prevalence and density of neutral hydrogen gas clouds in the galaxies.
• It aids in enumerating the temperature of gas clouds.
• Matching in redshift information helps to identify spectral lines of elements like helium, carbon, silicon, and the presence of other heavier element traces in the clouds.
• High column density clouds of neutral hydrogen atoms confirm the presence of damped Lyman-alpha systems.

Damped Lyman-alpha systems:

Damped Lyman alpha systems is a term used to specify the concentration of neutral hydrogen gas atoms detected in the quasar spectra, the most importantly employed in distant active galactic nuclei. These are the systems with hydrogen column density higher than 2X10²⁰ atoms/cm².

The Lyman alpha absorption lines of the neutral hydrogen atoms observed in the quasar spectra are broadened by radiation damping. These systems are associated with the early stages of galaxy formation and have relatively high redshifts of 2-4 when containing most of the neutral hydrogen in the universe. And they help to study the dynamics of early galaxies directly.

The Lyman alpha emitters:

The Lyman alpha emitters are distant galaxies that provide glimpses of the universe's history due to finite light velocity. And they emit Lyman alpha radiations. Narrow-band searches identify them because of their excess narrow-band flux at wavelengths interpreted in their redshifts.

The hydrogen atoms ionize due to the ongoing burst of stars. And their recombination form the Lyman alpha emitters. Bruce Partridge and P.J.E. Peebles first observed them in 1967 in young galaxies.

These are low-mass galaxies of 108 to 1010 solar masses with 200 to 600 million years old. And their star formation is specific when compared with any known galaxies. Because of all these properties, they were considered ancestors of Milky Way type galaxies.

The varying fractions of emitted Lyman-alpha radiations escape from the galaxies and are visible to distant viewers. It is evident that the dust of the galaxies is the vital factor for eluding the Lyman alpha photons. The association of redshifts with interstellar medium dust significantly contributes to these escape fractions. The continuous interplay of electromagnetic light radiations with neutral gas clouds leads to anisotropic distribution of density and velocity of hydrogen atoms. It stimulates the photons escape from the galaxies. 

In cosmological studies, the LAE redshift observations assist in tracing the dark matter halos and evolution of universe matter distribution.

Lyman-alpha blob:

Lyman-alpha blobs are the large gaseous structures known so far. Among which most of them had more than 400,000 light-years age. They were the massive Lyman-alpha line emitters found at high redshifts in the Universe due to the ultraviolet nature of Lyman-alpha.

Currently, we are unaware of how Lyman-alpha blobs help disclose the over densities of galaxies at high redshifts zones of the universe. Also, their connections with the surrounding galaxies and the mechanisms favouring the Lyman alpha emission are still unknown.

In 2000, Steidel et al. discovered the world's prominent Lyman-alpha blob. Additionally, in the original field of Steidel et al., more than 30 smaller Lyman alpha blobs were invented by Matsuda et al.

But, still, Lyman-alpha blobs research hint the formation of galaxies with valuable insights.

Gunn-Peterson trough:

James E. Gunn and Bruce Peterson first explained the suppression of electromagnetic emissions in quasar spectra in 1965.

At the redshift of the emitted light, due to presence of the neutral hydrogen gas atoms of intergalactic medium, a suppression of the electromagnetic emissions having wavelengths shorter than 121.56 nm observed from quasars. It shows the characteristic Gunn-Peterson trough in the quasar spectra.

The Gunn-Peterson trough was observed in 2001 by Robert Becker et al. in a quasar at a redshift of z=6.28. It happened nearly three decades after the theoretical prediction. And they found two more redshifts in the same quasar at z=5.82 and z=5.99. These redshifts showed absorptions at wavelengths on the blue side of the Lyman alpha transitions besides numerous spikes in energy distributions.

 At z=6.28, the quasar flux was effectively zero for wavelengths beyond the Lyman-alpha limit. It suggests the concentration of neutral hydrogen atoms present in the intergalactic medium might be approximately higher than 10-3.

In the analysis data, a trough seen at z=6.28 and the other two redshifts less than z<6 have no troughs. It confirmed that the reionization process of universe occurred at z=6.

The universe was expected to be neutral after recombination until the first celestial object emitted light energy. The released light radiation starts the reionization of the surrounding intergalactic hydrogen atoms. However, as the scattering cross-section of photons with energies near that of the Lyman-alpha limit with neutral hydrogen is very high, even a small fraction of neutral hydrogen will make the optical depth of the IGM high enough to cause the suppression of emission observed.

Questions and answers on the Lyman-alpha line concept:

How do you calculate the wavelength of the Lyman-alpha line in the quasar spectra?

Lyman-alpha is the first and the most prominent spectral line of the hydrogen spectrum. The plethora of hydrogen in the universe gave enormous importance to hydrogen spectral line observations remarkably to Lyman-alpha transitions.

The occurrence of hydrogen spectral emissions or absorptions in ultraviolet, visible, and infrared regions that occupy the predominant part of the electromagnetic spectrum added eminence to hydrogen spectrum investigations. Hence, in hydrogen spectral analysis, the calculation of spectral lines wavelengths is crucial to spot them.

As discussed, the Rydberg formula helps estimate the wavelengths of hydrogen spectral lines accurately.

The Rydberg equation

Additionally, the Lyman-alpha line exists in the Lyman series of the hydrogen spectrum. So, replacing the n1 and n2 values of the Rydberg formula with 1 and 2 will allow us to enumerate the Lyman-alpha photon's wavelengths.

The Lyman series formula

Why is Lyman-alpha the most intense spectral line of the Lyman series?

Lyman-alpha is a conspicuous spectral emission of celestial space. Even though it lies in the vacuum ultraviolet region, it is the bright spectral line of the earth's atmosphere. It is due to the abundance of hydrogen in the universe and substantial number of electron transitions corresponding to Lyman-alpha line.

The reason behind the high intensity of the Lyman-alpha line is due to increased number of electron transitions with 121.5 nm. It has to be reminded that intensity does not influence the number of spectral lines in the spectrum.

For instance, a suitable temperature condition promoted a more number of hydrogen electrons move from n=1 to n=2. Consequently, the enhanced the emission of Lyman-alpha photons.

When the energy of photon is greater than or equal to 10.2 eV available to hydrogen atom from an external source favors the Lyman-alpha transition, which influences the spectral line intensity.

Lyman-alpha energy calculation

As the ionization energy of hydrogen atom is 13.6 eV, most hydrogen atoms tend to favor Lyman-alpha absorptions rather than ionization. All these facts effects the intensity of Lyman-alpha line in hydrogen spectrum.

What is the Lyman-alpha transition?

Lyman series is one among the infinite spectral sequences of the atomic hydrogen spectrum. The U.S Physicist Theodore Lyman discovered the first spectral line of the Lyman series in 1906 during the electron transition from 1s-orbit to 2p-orbit of the hydrogen atom. He named it Lyman-alpha.

The Lyman-alpha doublet

The ground state hydrogen electron on the absorption of light energy undergoes excitation from 1s to 2p orbit. After being unstable, it returns to the original position with photon emission at 121.5 nm, which is the characteristic wavelength of the Lyman-alpha spectral line.

So, the Lyman-alpha transition is the electron's to and fro movement from 1s-orbit to 2p-orbit.

How do you calculate the frequency of the Lyman-alpha line?

The frequency of the Lyman-alpha line represents the number of Lyman-alpha radiations passing through the given point in a unit of time. Its SI unit is Hertz which is equivalent to one cycle per second. As the light radiations possess wave character, the Lyman-alpha being light radiations show all characteristic properties of the wave.

As we all know, frequency and wavelength are inversely proportional to each other. The frequency calculation of Lyman-alpha needs its wavelength value.

Frequency and wavelength relationship of the light radiation

Where,

ϒ = frequency of the light radiation

c = velocity of light in vacuum

λ = wavelength of the light

The Lyman-alpha line occurs at 121.5 nm in the ultraviolet region of the hydrogen spectrum. Its frequency calculation involves the following mathematical derivations;

Frequency calculation for Lyman-alpha line

Why does the Lyman-alpha line have the least energy in the Lyman series?

The Lyman-alpha line is the hydrogen spectral line that occurs in the Lyman series of the hydrogen spectrum. Due to the abundance of hydrogen gas in the universe, we can find this Lyman-alpha spectral line in quasar spectra when the neutral hydrogen atoms of the intergalactic medium absorb quasar photons having wavelengths like that of Lyman-alpha radiation.

Lyman-alpha line in quasar spectra

The electron transition from principal quantum number n=1 to n=2 gives the Lyman-alpha line in the quasar spectra. Due to the small energy gap between the two electron transition states, the Lyman-alpha emissions occur with the lowest energy changeovers compared with the other electron transitions of the Lyman series. Therefore, the Lyman-alpha spectral line occurs at the longest wavelength of 121.5 nm.

Conclusion:

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