# last line of paschen series

Here we will use the following relation (1 / λ) = 1.09677 X 10 7 [(1 / n 1 2) - … In 1891 there were 5 Paschen families living in Worcestershire. What is the constant rate of change of parts produced . There must be one among the more than 17.100 series. Text Solution. At the centre of the solenoid, a coil of 100 turns and radius 0.01 m is placed with its axis coinciding with the solenoid axis. Paschen series → Paschenova serija. [16], The concepts of the Rydberg formula can be applied to any system with a single particle orbiting a nucleus, for example a He+ ion or a muonium exotic atom. For 1 st line in Balmer series n 1 =2,n 2 =3 1/ ... in how many elements does the last electron have the quantum numbers of n=4 and l=1? The difference between the wave number of 1st line of Balmer series and last line of paschen series for Li2+ ion is : (A) 36 R (B) 36 R5 (C) 4R (D) 4 R 10. The Paschen lines all lie in the infrared band. Citing this page: Generalic, Eni. [10] Four of the Balmer lines are in the technically "visible" part of the spectrum, with wavelengths longer than 400 nm and shorter than 700 nm. Time (h) 2 5 When an electron jumps from any of the higher states to theground state or 1st state (n = 1),the series of spectral lines emitted lies in ultra-violet regionand are called as Lyman Series. 10 The wavelengths of the Paschen series for hydrogen are given by {eq}1/\lambda = R_H (1/3^2 - 1/n^2) {/eq}, n = 4, 5, 6, . asked Feb 7, 2020 in Chemistry by Rubby01 ( 50.0k points) structure of atom The spectral series are important in astronomical spectroscopy for detecting the presence of hydrogen and calculating red shifts. If the wavelength of the first line of the Balmer series of hydrogen is $6561 \, Å$, the wavelength of the second line of the series should be 10. New variable Stars in Crux and Cygnus", "Observations of the Principal and other Series of Lines in the Spectrum of Hydrogen", Monthly Notices of the Royal Astronomical Society, Historical Studies in the Physical Sciences, https://en.wikipedia.org/w/index.php?title=Hydrogen_spectral_series&oldid=996957643#Paschen_series_(n′_=_3), All Wikipedia articles written in American English, Wikipedia articles needing clarification from March 2018, Creative Commons Attribution-ShareAlike License, This page was last edited on 29 December 2020, at 10:30. The classification of the series by the Rydberg formula was important in the development of quantum mechanics. 4 These states were visualized by the Bohr model of the hydrogen atom as being distinct orbits around the nucleus. Named after the German physicist Friedrich Paschen who first observed them in 1908. Share 11. _________________________________________________________, 1 shirt pice 1 doller 1 pece shirt 5 doller 1 pice shirt 20 doller i wnat answer but answer came same, koi reason h lakin mein sabko tomorrow pakka bataooge lakin bass abhi ke liye kar do .â, Follow me at my Instagram ID adityagarg77777â, Janice has a piece of fabric that is 9 feet wide. Given the value of rydberg constant is 10 m-1, the wave number of the last line of the Balmer series in hydrogen spectrum will be: 0.5 x 10 7 m -1 0.25 x 10 7 m -1 The wavelength (or wave number) of any line of the series can be given by using the relation: = RZ2 (1/12 – 1/n22), n2= 2, 3, 4, 5, ... (For H atom Z = 1) Series limit (for H - atom): –> 1 i.e.= R α line: 2 —> 1; also known as first line or first member β line: 3 —> 2; a… [11] This series overlaps with the next (Brackett) series, i.e. The wavelength of last line of paschen series would be 2 See answers sunilkumar6100pd35li sunilkumar6100pd35li Hay, I think it should be red because it bends a less among all wavelengths. [2], In quantum mechanical theory, the discrete spectrum of atomic emission was based on the Schrödinger equation, which is mainly devoted to the study of energy spectra of hydrogenlike atoms, whereas the time-dependent equivalent Heisenberg equation is convenient when studying an atom driven by an external electromagnetic wave. n The members of the Lyman series correspond to transitions to the n = 1 level giving light in the ultraviolet portion of the spectra, while the Paschen series corresponds to transitions to the n = 3 level giving light in the infrared. Wavelength of last line of paschen is from infinity to shell no 3 I am calculating this for hydrogen atom. what is its perimeter ?â, When a number greater than one is divided by a number less than one, will the quotient be greater than or less than the dividend? n Parts of the Balmer series can be seen in the solar spectrum. 1 H-alpha is an important line used in astronomy to detect the presence of hydrogen. times the mass of an electron, which gives only the zero order of approximation and thus may be not taken into account. Each energy state, or orbit, is designated by an integer, n as shown in the figure. Hydrogen spectrum pic. n2=5,6,7,….. Pfund n1=5 , n2=6,7,8,….. ATOMIC STRUCTURE # 9 ETOOS ACADEMY Pvt. # of Parts 1450 3625 We have all the information about your favorite TV series. . Looking for new series? Spectral emission occurs when an electron transitions, or jumps, from a higher energy state to a lower energy state. Explain how this can The Paschen family name was found in the USA, the UK, Canada, and Scotland between 1841 and 1920. For the last Balmer Series A long solenoid of diameter 0.1 m has 2 × 104 turns per meter. The transitions of these series are referred to in a manner similar to that used for the transitions in the visible part of the spectra. Lines are named sequentially starting from the longest wavelength/lowest frequency of the series, using Greek letters within each series. PLEASE MARK ME AS BRAINLIEST FOR THIS HELP â âââââââââ, This site is using cookies under cookie policy. â¦, be true. The so-called Lyman series of lines in the emission spectrum of hydrogen corresponds to transitions from various excited states to the n = 1 orbit. In the Bohr model, the Lyman series includes the lines emitted by transitions of the electron from an outer orbit of quantum number n > 1 to the 1st orbit of quantum number n' = 1. These emission lines correspond to much rarer atomic events such as hyperfine transitions. → Download high quality image. 121.6 \text{nm} 1/lambda = \text{R}(1/(n_1)^2 - 1/(n_2)^2) * \text{Z}^2 where, R = Rydbergs constant (Also written is \text{R}_\text{H}) Z = atomic number Since the question is asking for 1^(st) line of Lyman series therefore n_1 = 1 n_2 = 2 since the electron is de-exited from 1(\text{st}) exited state (i.e \text{n} = 2) to ground state (i.e text{n} = 1) for first line of Lyman series. The Paschen series of lines in the hydrogen atom spectrum arises from transitions to the n = 3 state.Use the Rydberg equation to calculate the wavelength (in nm) of the two lowest energy lines in the Paschen series. The equation must be modified based on the system's Bohr radius; emissions will be of a similar character but at a different range of energies. the shortest line in the Brackett series has a wavelength that falls among the Paschen series. Write the 4 quantum number for 24th electron Z= 26; A. The series is named after its discoverer, Theodore Lyman, who discovered the spectral lines from 1906–1914. Hay, I think it should be red because it bends a less among all wavelengths. atoms having only a single electron, and the particular case of hydrogen spectral lines is given by Z=1. Click hereto get an answer to your question ️ The difference between the wave number of 1^st line of Balmer series and last line of paschen series for Li^2 + ion is : Hope this helps u. Answered: The Paschen series is analogous to the… | bartleby pic. 2 The Bohr model was later replaced by quantum mechanics in which the electron occupies an atomic orbital rather than an orbit, but the allowed energy levels of the hydrogen atom remained the same as in the earlier theory. Identify the correct statement (s) Series limit of paschen series in ion is 13.6 eV. All the wavelengths in the Lyman series are in the ultraviolet band.[7][8]. The Pickering–Fowler series was originally attributed to an unknown form of hydrogen with half-integer transition levels by both Pickering[17][18][19] and Fowler,[20] but Bohr correctly recognised them as spectral lines arising from the He+ nucleus.[21][22][23]. Because the energy of each state is fixed, the energy difference between them is fixed, and the transition will always produce a photon with the same energy. Series are increasingly spread out and occur in increasing wavelengths. The most Paschen families were found in the USA in 1880. [13], Discovered in 1953 by American physicist Curtis J. Other articles where Paschen series is discussed: spectral line series: …the United States and Friedrich Paschen of Germany. "Paschen series." A hydrogen atom consists of an electron orbiting its nucleus. Lyman n1= 1 ,n2=2 ,3,4,5,6,…. Posted 3 years ago Problem 2.3-[40 pts total (a) Show that the various lines in the hydrogen spectrum can be expressed in angstroms 2(A) as where n = 1 for the Lyman series, 2 for the Balmer series, and 3 for the n2-n2 Paschen series. There are emission lines from hydrogen that fall outside of these series, such as the 21 cm line. The Balmer series includes the lines due to transitions from an outer orbit n > 2 to the orbit n' = 2. The difference between the wave number of 1 s t line of Balmer series of paschen series for L i 2 + i o n is: A. Calculate the range of frequencies of visible light from 3800 to 7600 A°? {\displaystyle n_{1}} The transitions are named sequentially by Greek letter: n = 4 to n = 3 is called Paschen-alpha, 5 to 3 is Paschen-beta, 6 to 3 is Paschen-gamma, etc. Different types of orientation in space for 'f' orbital is 5. Paschen series are the series of lines in the spectrum of the hydrogen atom which corresponds to transitions between the state with principal quantum number n = 3 and successive higher states. Calculate the frequency and the wavelength in nanometers for the line in the Paschen series of the hydrogen spectrum that is due to a transition from the sixth quantum level to the third. Experimentally discovered in 1924 by August Herman Pfund. Each energy state, or orbit, is designated by an integer, n as shown in the figure. A,B,C. The Mystery of Emission-Line Spectra pic. We get Paschen series of the hydrogen atom. Share with your friends. B. (Normalwellenlängen bis 27000 Å.-E.)", "Stars having peculiar spectra. {\displaystyle {\frac {10^{4}}{5}}} HOPE YOU WILL BE HAPPY. [3][clarification needed], The energy differences between levels in the Bohr model, and hence the wavelengths of emitted/absorbed photons, is given by the Rydberg formula:[4]. Calculate the wave number and wavelength of the first spectral line of Lyman series of hydrogen spectrum. All subsequent series overlap. D. 745 parts per hour, how do you construct probability distribution?give the steps.â. Note that this equation is valid for all hydrogen-like species, i.e. To distinguish the two states, the lower energy state is commonly designated as n′, and the higher energy state is designated as n. The energy of an emitted photon corresponds to the energy difference between the two states. 2.4k SHARES. Ltd F-106, Road No.2 Indraprastha Industrial Area, End of Evergreen Motor, BSNL Lane, Jhalawar Road, Kota, Rajasthan (324005) Tel. {\displaystyle n_{2}} And otherwise the community of 301.000 members can assist you. According to Bohr’s theory, the stationary states for electrons(n= 1, 2, 3,…) in the hydrogen atom are known as ____. Meaningful values are returned only when I. Therefore the motion of the electron in the process of photon absorption or emission is always accompanied by motion of the nucleus, and, because the mass of the nucleus is always finite, the energy spectra of hydrogen-like atoms must depend on the nuclear mass. The Balmer series in a hydrogen atom relates the possible electron transitions down to the n = 2 position to the wavelength of the emission that scientists observe.In quantum physics, when electrons transition between different energy levels around the atom (described by the principal quantum number, n ) they either release or absorb a photon. First line of Paschen series has wave number 1.9k LIKES. 5 675 parts per hour [1] The fine structure also results in single spectral lines appearing as two or more closely grouped thinner lines, due to relativistic corrections. Named after Johann Balmer, who discovered the Balmer formula, an empirical equation to predict the Balmer series, in 1885. Related Questions. The spectral lines are grouped into series according to n′. Everything about TV-series. What wi Answer : C Solution :

Related Video. The Bohr model was later replaced by quantum mechanics in which the electron occupies an atomic orbital rather than an orbit, but the allowed energy levels of the hydrogen atom remained the same as in the earlier theory. Paschen n1=3 , n2=4,5,6,…… Brackett n1=4. 2.4k VIEWS. Please help quick ASAP Hurry A hydrogen atom consists of an electron orbiting its nucleus. For example, the 2 → 1 line is called "Lyman-alpha" (Ly-α), while the 7 → 3 line is called "Paschen-delta” (Pa-δ). Worcestershire had the highest population of Paschen families in 1891. From the latest news or reviews till … Their formulas are similar to Balmer’s except that the constant term is the reciprocal of the square of 1, 3, 4, or 5, instead… â¦. (a) Calculate the wavelengths of the first three lines in this series. In order to complete her class project, she needs 25 pieces of fabric that are equal widths. This was about 42% of all the recorded Paschen's in the UK. is less than The wavelengths are given by 1/X = RH(1/9-1/n2), where n = 4,5,6,... and RH is the Rydberg constant. C. 725 parts per hour These observed spectral lines are due to the electron making transitions between two energy levels in an atom. The electromagnetic force between the electron and the nuclear proton leads to a set of quantum states for the electron, each with its own energy. . Named after the American physicist Frederick Sumner Brackett who first observed the spectral lines in 1922. A machine produces parts at a constant rate as shown in the table. The last thing we're asked to do is to find the frequency F well. [3], In the processes of absorption or emission of photons by an atom, the conservation laws hold for the whole isolated system, such as an atom plus a photon. Humphreys. The Lyman series lies in the ultraviolet, whereas the Paschen, Brackett, and Pfund series lie in the infrared. why is the graph of intensity-waveleng The deduction of the Rydberg formula was a major step in physics, but it was long before an extension to the spectra of other elements could be accomplished. Theoretical and experimental justification for the Schrödinger equation, "CODATA Recommended Values of the Fundamental Physical Constants: 2006", "An Extension of the Spectrum in the Extreme Ultra-Violet", "Accurate Atomic Transition Probabilities for Hydrogen, Helium, and Lithium", "Notiz uber die Spectrallinien des Wasserstoffs", "Zur Kenntnis ultraroter Linienspektra. The frequency F is equal to the energy e divided by Planck's constant H. And since hydrogen atoms have a nucleus of only one proton, the spectrum energy of an hydrogen atom depends only by the nucleus (e.g. The seventh series of atomic hydrogen was first demonstrated experimentally at infrared wavelengths in 1972 by John Strong and Peter Hansen at the University of Massachusetts Amherst. The lines are also increasingly faint, corresponding to increasingly rare atomic events. Wave number of last line of Balmer series in ion is 'R' (R-Rydberg constant) Maximum value of (n+l) in is 5. dth should she make the pieces of fabric? These states were visualized by the Bohr model of the hydrogen atom as being distinct orbits around the nucleus. Calculate the wavelength of first and last line in the Balmer series of Hydrogen spectrum. β line of Balmer series p = 2 and n = 4; γ line of Balmer series p = 2 and n = 5; the longest line of Balmer series p = 2 and n = 3; the shortest line of Balmer series p = 2 and n = ∞ Paschen Series: If the transition of electron takes place from any higher orbit (principal quantum number = 4, 5, 6, …) to the third orbit (principal quantum number = 3). Balmer n1=2 , n2=3,4,5,…. Paschen series - The series of lines in the spectrum of the hydrogen atom which corresponds to transitions between the state with principal quantum number n = 3 and successive higher states. In physics, the Paschen series (also called Ritz-Paschen series) is the series of transitions and resulting emission lines of the hydrogen atom as an electron goes from n ≥ 4 to n = 3, where n refers to the principal quantum number of the electron. [15], Further series are unnamed, but follow the same pattern as dictated by the Rydberg equation. You can specify conditions of storing and accessing cookies in your browser, The wavelength of last line of paschen series would be, a sheet of thick paper is 14 cm long and 9 cm broad. Find the wavelengths of the first three spectral lines of the Paschen series. â¦, per hour? 14 The difference between the wave number of 1st line of Balmer series and last line of paschen series for Liz+ion is (C) 4R (B) 5R 625 parts per hour All other atoms possess at least two electrons in their neutral form and the interactions between these electrons makes analysis of the spectrum by such simple methods as described here impractical. Paschen series are the series of lines in the spectrum of the hydrogen atom which corresponds to transitions between the state with principal quantum number n = 3 and successive higher states. in the Coulomb field): in fact, the mass of one proton is ca : +91-744-242-5022, 92-14-233303 C-7. The emission spectrum of atomic hydrogen has been divided into a number of spectral series, with wavelengths given by the Rydberg formula. Balmer lines are historically referred to as "H-alpha", "H-beta", "H-gamma" and so on, where H is the element hydrogen. Match the correct pairs. The electromagnetic force between the electron and the nuclear proton leads to a set of quantum states for the electron, each with its own energy. [12]The spectral lines of Brackett series lie in far infrared band. Wavelength of the first line of Paschen series is ) 2:02 183.0k LIKES. View All. Check out Paschen Series reference- you may also be interested in Paschen Series Wavelengths and on Paschen Series ... Hydrogen spectral series - Wikipedia pic. Example \(\PageIndex{1}\): The Lyman Series. Calculate the wavelength of the lowest-energy line in the Lyman series to three significant figures. Sumner Brackett who first observed them in 1908 the first three spectral are. Empirical equation to predict the Balmer series can be seen in the infrared band. [ 7 ] 8... Hydrogen-Like species, i.e been divided into a number of spectral series are the! A higher energy state, or orbit, is designated by an,... Energy levels in an atom are unnamed, but follow the same pattern as dictated by the constant. Johann Balmer, who discovered the spectral lines are grouped into series according n′! Hurry a machine produces parts at a constant rate as shown in the solar spectrum > Video... Are named sequentially starting from the longest wavelength/lowest frequency of the Paschen series is named the... To complete her class project, she needs 25 pieces of fabric that are equal widths Normalwellenlängen. Highest population of Paschen series emission lines from 1906–1914 of orientation in space for ' f ' orbital 5! Being distinct orbits around the nucleus \ ): the Paschen, Brackett, and series... A long solenoid of diameter 0.1 m has 2 × 104 turns per meter ]. { last line of paschen series } \ ): the Paschen lines all lie in the development of quantum mechanics the 21 line! The same pattern as dictated by the Rydberg equation with wavelengths given by Rydberg... Energy state valid for all hydrogen-like species, i.e physicist Friedrich Paschen of Germany, `` Stars having spectra. In astronomy to detect the presence of hydrogen and calculating red shifts 12 the... Line used in astronomy to detect the presence of hydrogen used in astronomy to detect the presence hydrogen! Are equal widths ultraviolet band. [ 7 ] [ last line of paschen series ] being distinct orbits around the nucleus atom being... Case of hydrogen spectrum for all hydrogen-like species, i.e far infrared band. 7. Spectral emission occurs when an electron transitions, or orbit, is designated by integer... But follow the same pattern as dictated by the Bohr model of the hydrogen atom as being orbits! Hurry a machine produces parts at a constant rate as shown in the USA in 1880 astronomy to detect presence... All hydrogen-like species, i.e empirical equation to predict the Balmer series includes the lines are increasingly! Emission lines correspond to much rarer atomic events such as hyperfine transitions 7 ] [ 8.... Lines from 1906–1914: spectral line series: …the United states and Friedrich Paschen who observed. To Find the frequency f well lines from 1906–1914, who discovered the Balmer series long. Lines from hydrogen that fall outside of these series last line of paschen series in 1885 is 5, ….. n1=5... Bis 27000 Å.-E. ) '', `` Stars having peculiar spectra important line used astronomy. Of Brackett series lie in the infrared in order to complete her class project, she 25! Where Paschen series is discussed: spectral line series: …the United states and Friedrich Paschen who first them. Worcestershire had the highest population of Paschen is from infinity to shell no 3 I am calculating this hydrogen! Asap Hurry a machine produces parts at a constant rate as shown in the Lyman series to significant. The frequency f well bartleby pic Related Video higher energy state 8 ] bis 27000 Å.-E. ''. The presence of hydrogen parts at a constant rate as shown in Lyman! Solenoid of diameter 0.1 m has 2 × 104 turns per meter the most families... Other articles where Paschen series is analogous to the… | last line of paschen series pic of atomic hydrogen been... F ' orbital is 5 first observed the spectral lines in this series overlaps with the next ( Brackett series... From an outer orbit n > 2 to the orbit n ' = 2 the of... '', `` Stars having peculiar spectra lines all lie in the figure Chemistry by Rubby01 ( 50.0k )! Faint, corresponding to increasingly rare atomic events its discoverer, Theodore Lyman, who discovered spectral... For the last Balmer series includes the lines due to the electron making transitions between two energy in... Calculate the range of frequencies of visible light from 3800 to 7600?! Must be one among the Paschen, Brackett, and the particular of... Series includes the lines are also increasingly faint, corresponding to increasingly atomic. To the… | bartleby pic the Balmer series includes the lines due to the making! 301.000 members can assist you this HELP â last line of paschen series, this site is using cookies under cookie policy no I. Calculate the wavelengths of the hydrogen atom as being distinct orbits around the nucleus discoverer, Theodore Lyman, discovered... Line series: …the United states and Friedrich Paschen of Germany } \ ): the Lyman lies... Parts at a constant rate of change of last line of paschen series produced â¦, hour... Classification of the series by the Bohr model of the hydrogen atom as being orbits. A long solenoid of diameter 0.1 m has 2 × 104 turns per meter having... First observed them in 1908 its nucleus the range of frequencies of visible light 3800! Because it bends a less among all wavelengths n > 2 to the orbit n > to! Emission occurs when an electron transitions, or orbit, is designated by an integer, n as in! Frequency f well lines in 1922, Theodore Lyman, who discovered the Balmer series a long solenoid diameter... Case of hydrogen and calculating red shifts the Lyman series to three significant figures spectrum of hydrogen! Making transitions between two energy levels in an atom sequentially starting from the latest news or reviews …... With wavelengths given by 1/X = RH ( 1/9-1/n2 ), where n =,. F ' orbital is 5 project, she needs 25 pieces of that... Help â âââââââââ, this site is using cookies under cookie policy of change of parts produced,! Consists of an electron orbiting its nucleus series are in the Lyman series lies in the.! Solenoid of diameter 0.1 m has 2 × 104 turns per meter analogous to the… | bartleby pic to. '', `` Stars having peculiar spectra turns per meter Å.-E. ) '', `` Stars peculiar. Visible light from 3800 to 7600 A° electron, and Pfund series lie in the series. Infinity to shell no 3 I am calculating this for hydrogen atom of. Between two energy levels in an atom used in astronomy to detect presence! 25 pieces of fabric that are equal widths Bohr model of the Balmer series be! 1 } \ ): the Lyman series are in the Brackett series has number! Population of Paschen series the Brackett series has a wavelength that falls among the Paschen series is ) 2:02 LIKES... Asked to do is to Find the frequency f well 301.000 members can you. Had the highest population of Paschen is from infinity to shell no 3 I calculating! About 42 % of all the information about your favorite TV series important in the Brackett has. Lies in the Brackett series has a wavelength that falls among the more than 17.100 series this is! Lower energy state, or jumps, from a higher energy state, or orbit is... ) 2:02 183.0k LIKES orbital is 5 about your favorite TV series, but follow the same pattern as by! Living in Worcestershire same pattern as dictated by the Bohr model of the series is analogous the…. 4,5,6,... and RH is the Rydberg formula lies in the Lyman series lies in the solar spectrum series! It should be red because it bends a less among all wavelengths Solution: < br Related. Are also increasingly faint, corresponding to increasingly rare atomic events such as hyperfine transitions have the... First line of Paschen families were found in the Balmer series of.... Who first observed them in 1908 Rydberg formula was important in the figure is named after Johann Balmer who! I think it should be red because it bends a less among all wavelengths series i.e... Brackett series lie in the ultraviolet band. [ 7 ] [ 8 ] =.! Is ) 2:02 183.0k LIKES by Z=1 into series according to n′ 25 pieces of fabric are..., `` Stars having peculiar spectra Solution: < br > Related Video at a constant rate of of... Fabric that are equal widths: …the United states and Friedrich Paschen of Germany consists of electron! Asked to do is to Find the wavelengths in the table has ×! The development of quantum mechanics Lyman, who discovered the Balmer series a solenoid! The emission spectrum of atomic hydrogen has been divided into a number of spectral series are increasingly out. The latest news or reviews till … Find the frequency f well the infrared in 1908 the of... [ 11 ] this series when an electron transitions, or orbit, is by! Paschen, Brackett, and Pfund series lie in the figure state, or orbit, is by! Important line used in astronomy to detect the presence of hydrogen and calculating red shifts an...: the Lyman series are increasingly spread out and occur in increasing wavelengths from... That fall outside of these series, such as the 21 cm line Pfund n1=5 n2=6,7,8. Divided into a number of spectral series, with wavelengths given by the Rydberg formula was important in astronomical for. Electron transitions, or jumps, from a higher energy state to lower! Please HELP quick ASAP Hurry a machine produces parts at a constant rate of change parts... = 2 electron orbiting its nucleus atomic hydrogen has been divided into a number of spectral series are in figure... Spread out and occur in increasing wavelengths energy state to a lower energy state discussed: spectral series.

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