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Spectral series are the collection of wavelengths arranged in a sequential order. These are in the form of lines. The spectral series can be calculated by using the Rydberg formula. Let’s understand the spectral series and spectral series of the hydrogen atoms.
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Key Terms: Spectral series, hydrogen spectrum series, rydberg equation, Wavelength, Atom, Hydrogen, Atomic system, Radiation, Spectroscope, Light, Ultraviolet ray
Spectral Series
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Studying Hydrom atom is the easiest way to understand the basic principle of the Spectral series. The hydrogen atom is the most basic atomic system found in nature. It produces the most basic spectral series. Each component of the light or radiation forms an image of the source when a slit allows a beam of light or other radiation to enter the device. These images can be seen with a spectroscope.
The spectral lines are arranged next to each other in the form of parallel lines with consistent spacing. When moving from a higher to a lower wavelength, the lines formed will be apart in the higher wavelength side and closer in the lower wavelength side. The wavelengths of the Lyman series are all in the Ultraviolet band.
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How Spectral Series are Formed?
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Bohr's atomic model explains the set of energy levels/states that each atom encloses. Quantum numbers (n=1,2,3,4,5,6,.....) are used to name energy states. A photon of energy nh – nl is released when electrons jump from higher energy states (nh) to lower energy ones (nl). The transition between similar energy states that produces the same energy photon is observed because the energy associated with each state is fixed and has differences between them
The electron transition to a lower energy state divides the spectral series into equivalent series. Within the series, the Greek alphabets are utilized to separate the spectral lines of corresponding energy.
Rydberg formula
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The emission spectrum is displayed by the atomic hydrogen. This spectrum is made up of numerous different spectral series. The electrons in the gas make transitions between energy levels once they reach the excited state. These spectral lines are the result of Neils Bohr's model of electron transitions between energy levels. The Rydberg formula is used to calculate the wavelengths of the spectral series.
The energy difference between the various levels of Bohr's model and the wavelengths of absorbed or emitted photons is represented by the Rydberg formula. It can be stated mathematically as-
1/λ = RZ2(1/n12− 1/n2h)
Where,
λ is the wavelength
R is the Rydberg constant which has a value of 1.09737107 m-1
Z is the atomic number
The lower energy level is nl,
And the higher energy level is nh.
Types of Spectral Series
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Lyman series (nl=1)
The series was discovered by Theodore Lyman during the years 1906 and 1914. As a result, these series are named after him. According to Bohr's model, when electrons transition takes place from higher energy states (nh=2,3,4,5,6,...) to nl=1 energy state, the Lyman series appears. The wavelengths of the Lyman series are all in the Ultraviolet band.
| Energy level (n) | Wavelength (in nanometers) in vacuum |
|---|---|
| ∞ | 91.175 |
| 6 | 93.78 |
| 5 | 94.974 |
| 4 | 97.256 |
| 3 | 102.57 |
| 2 | 121.57 |
Balmer series (nl=2)
Johann Balmer discovered the Balmer series in the year 1885.
The Balmer series appears when electrons shift from higher energy levels (nh=3,4,5,6,7,...) to the lower energy state (nl=2). The Balmer series' wavelengths are all visible in the electromagnetic spectrum (400nm to 740nm). Hydrogen is detected in astronomy using the H-Alpha line of the Balmer series, which is also a part of the solar spectrum.
| Energy level (n) | Wavelength in air |
|---|---|
| ∞ | 364.6 |
| 7 | 397.0 |
| 6 | 410.2 |
| 5 | 434.0 |
| 4 | 486.1 |
| 3 | 656.3 |
Paschen series (nl=3)
Friedrich Paschen, a German physicist, was the first to notice the series in 1908. As a result, the series bears his name. When electrons migrate from higher energy levels (nh=4,5,6,7,8,...) to lower energy states (nl=3), the Paschen series appears. The Paschen series' wavelengths are all in the infrared range of the electromagnetic spectrum. The next series' smallest wavelength, i.e. the Brackett series, overlaps with the Paschen series. All succeeding series overlap with this one.
| Energy level (n) | Wavelength in air |
|---|---|
| ∞ | 820.4 |
| 8 | 954.6 |
| 7 | 1005 |
| 6 | 1094 |
| 5 | 1282 |
| 4 | 1875 |
Brackett series (nl=4)
Friedrich Sumner Brackett, an American physicist, first noticed the series in the year 1922. The Brackett series appears when electrons shift from higher energy levels (nh=5,6,7,8,9...) to lower energy states (nl=4). The Brackett series wavelengths are all in the infrared part of the electromagnetic spectrum.
| Energy level (n) | Wavelength in air |
|---|---|
| ∞ | 1458 |
| 9 | 1817 |
| 8 | 1944 |
| 7 | 2166 |
| 6 | 2625 |
| 5< | 4051 |
Pfund series (nl=5)
August Harman Pfund noticed the series for the first time in 1924. As a result, the Pfund series is named after him. When an electron transitions from a higher energy state (nh=6,7,8,9,10,...) to a lower energy state (nl=5), the Pfund series appears. Pfund series wavelengths are all in the infrared part of the electromagnetic spectrum.
| Energy level (n) | Wavelength in vacuum |
|---|---|
| ∞ | 2279 |
| 10 | 3039 |
| 9 | 3297 |
| 8 | 3741 |
| 7 | 4654 |
| 6 | 7460 |
Humphreys series (nl=6)
Curtis J Humphreys, an American physicist discovered these series in 1953. It has been observed that when electrons migrate from higher energy levels (nh=7,8,9,10,11...) to the lower energy state (nl=6), the Humphreys series appears. Wavelengths of the Humphreys series are all in the infrared portion of the electromagnetic spectrum.
| Energy level (n) | Wavelength in vacuum |
|---|---|
| ∞ | 3.282 |
| 11 | 4.673 |
| 10 | 5.129 |
| 9 | 5.908 |
| 8 | 7.503 |
| 7 | 12.37 |
Things to Remember
- Spectral series are the collection of wavelengths arranged in a sequential order.
- The hydrogen atom is the most basic atomic system found in nature.
- It produces the most basic spectral series.
- The energy difference between the various levels of Bohr's model and the wavelengths of absorbed or emitted photons is represented by the Rydberg formula. It can be stated mathematically as- 1/λ = RZ2(1/n12− 1/n2h)
- There are six types of spectral series- Lyman, Balmer, Paschen, Brackett, Pfund, and Humphreys.
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Sample Questions
Ques: Explain Balmer Series. (1 Mark)
Ans: The transition of electrons from any high energy level (n=3,4,5,6,... ) to the second energy level (p=2) produces spectral lines in the Balmer series. This series' wavelength falls inside the visible range of the electromagnetic spectrum.
Ques: What is Spectral Series? (1 Mark)
Ans When an electric discharge is sent through hydrogen gas, hydrogen molecules dissociate, resulting in excited (extremely energetic) hydrogen atoms that emit a specific frequency of radiation before reverting to their ground state. This is called as Spectral Series.
Ques: Name some of the types of Spectral series? (1 Mark)
Ans: Some of the spectral series are the Balmer series, Lyman series, Paschen series, Bracket series, Pfund series.
Ques: Describe the Pfund series and its mathematical formula. (2 Marks)
Ans: When an electron transitions from a higher energy state (nh=6,7,8,9,10,...) to a lower energy state (nl=5), the Pfund series appears. Pfund series wavelengths are all in the infrared part of the electromagnetic spectrum.
Mathematically expressed as
\(\frac{1}{\lambda} = (\frac{1}{5^2} - \frac{1}{n^2})\)
Ques: When a hydrogen atom absorbs a photon, it is excited to the n=4 level from its ground state. What are the photon's wavelength and frequency? (2 Marks)
Ans: Given, n =4
From Balmer series, we can write
1/λ = R(1/22 – 1/42) = 109677(1/4 – 1/16)
λ = 16/(3×109677) = 4.86×10-5cm (ans)
For frequency(υ), we know that it is given by the formula
υ =c/\(\lambda\) = 3×108/(4.86×10-7)
= 6.1×1014Hz
Ques: How Many Spectral Lines Can be Observed in the Spectrum? (2 Marks)
Ans: When the transitions take place from higher energy levels to lower energy levels, then spectral lines are observed. The fourth energy level elements transition to the third level, and then two second-level further moves on to the first. So, to observe spectral lines, the transition has to take place to lower levels.
Ques: Mention Various Series of the Spectrum and Different Parts of the Spectrum Where the Lines Fall. (3 Marks)
Ans: The various series of the spectrum and different parts of the spectrum where the lines fall -
- Lyman Series - Ultraviolet band. (UV band)
- Balmer series – Alpha line of Hydrogen
- Paschen Series - Infrared region (IR Region)
- Brackett Series - Infrared region (IR Region) and forms an electromagnetic spectrum. (EM spectrum)
- P-fund series - Infrared region (IR Region)
- Humphreys series- Infrared region. (IR Region)
Ques: How Many Spectral Lines are there? (3 Marks)
Ans: The lines that are seen when the electron transitions take place from higher energy levels to lower energy levels are spectral lines. The two types of spectral lines are as follows -
Emission lines: The emission lines are the type of spectral lines that may appear with discrete colours and have a black background. These lines are seen only when the particles emit the wavelength.
Absorption lines: These are another type of spectral lines. These may appear in the form of dark color bands and have a black background. These lines are seen only when the particles absorb the wavelengths.
Previous Year Questions
Ques: Define ionization energy. What is its value for a hydrogen atom? (All India 2010, 1 Mark)
Ans: Ionisation energy: It is the energy required to remove an electron from the outermost orbit of an atom. E.g.- It is -13.6 eV for hydrogen atom.
Ques: Write the expression for Bohr’s radius in the hydrogen atom. (Delhi 2010, 1 Mark)
Ans: The expression for Bohr’s radius in the hydrogen atom is-
radius:
r1 = \(\frac{\epsilon_0 h^2}{\pi me^2}\) = 0.529 x 10-10 m
Ques: The ground state energy of a hydrogen atom is -13.6 eV. What are the kinetic and potential energies of electrons in this state? (All India 2010, 1 Mark)
Ans: Kinetic energy, K.E.= T.E. = 13.6 eV
Potential energy, P.E. = 2 T.E. = 2 (-13.6) = – 27.2 eV
Here, T.E. is for Total Energy.
Ques: (i) When is the Ha line of the Balmer series in the emission spectrum of hydrogen atom obtained?
(ii) What is the maximum number of spectral lines emitted by a hydrogen atom when it is in the third excited state? (Compt. All India 2012, 2 Marks)
Ans: (i) When an electron jumps to the second orbit (n1 = 2) from any orbit n2 = n > 2, then the Balmer series is obtained.
(ii) For third excited state, n2 = 4, and n1 = 3, 2, 1 Hence maximum 3 spectral lines are there.
Ques: Using Bohr’s postulates of the atomic model, derive the expression for radius of nth electron orbit. Hence obtain the expression for Bohr’s radius. (All India 2012, 5 Marks)
Ans: Basic postulates of Bohr’s atomic model:
(i) Every atom consists of a central core called nucleus in which entire positive charge and mass of the atom are concentrated. A suitable number of electrons revolve around the nucleus in circular orbit. The centripetal force required for revolution is provided by the electrostatic force of attraction between the electron and the nucleus.
(ii) Electron can resolve only in certain discrete non-radiating orbits, called stationary orbit. Total angular momentum of the revolving electron in an integral multiple of h/2π.
… where [h is plank constant]
\(mvr = \frac{nh}{2\pi}\)
(iii) The radiation of energy occurs only when an electron jumps from one permitted orbit to another. The difference in the total energy of electrons in the two permitted orbits is absorbed when the electron jumps from inner to outer orbit and emitted when the electron jumps from outer to inner orbit.
To derive an expression for radii of Bohr’s stationary orbits-
According to Bohr’s postulates, the angular momentum of electron for any permitted orbit is,
\(mvr = \frac{nh}{2\pi}\) or \(v= \frac{nh}{2\pi mr}\) ….(i)
Also, according to Bohr’s postulates, the centripetal force is equal to the electrostatic force between the electron and nucleus.
Ques: The value of a ground state energy of a hydrogen atom is -13.6 eV.
(i) Find the energy required to move an electron from the ground state to the first excited state of the atom.
(ii) Determine
(a) the kinetic energy and
(b) orbital radius in the first excited state of the atom. (Given the value of Bohr radius = 0.53 Å) (Compt. All India 2014, 5 Marks)
Ans:
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