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The hydrogen spectrum is a form of electromagnetic radiation in which an electric discharge passes through gaseous hydrogen molecules. The gas dissolves, and the hydrogen atom goes into an excited state and passes different radiations.
- Each radiation consists of individual lines with well-defined wavelengths called hydrogen spectrum lines.
- When electrons are provided with the required energy, they get excited and move from a lower to a higher energy level.
- The origin of the spectrum can be explained with the help of Bohr’s model.
- The hydrogen spectrum is divided into various spectral series, such as Lyman and Balmer, which is given by the Rydberg formula.
- Electrons in the hydrogen atom will circle around the nucleus due to electromagnetic force between the proton and electron.
- The concept is used in astronomy as most of our universe is made of hydrogen atom.
Key Terms: Hydrogen Spectrum, Spectrum, Bohr’s Model, Rydberg Formula, Electromagnetic Force, Lyman Series, Balmer Series, Paschen Series, Bracket Series, Hydrogen Emission Spectrum
What is Hydrogen Spectrum?
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The hydrogen spectrum is also known as the hydrogen emission spectrum, in which excited electrons return back to their original level and emit radiation. This form of spectrum can be represented using spectral lines and wavelength.
- It helps in explaining the quantized electronic structure of an atom.
- The spectrum involves the dissociation of hydrogen atoms due to the discharge of electric current.
- The visible light spectrum is considered the subset of the hydrogen spectrum.
- Bohr model is modified with the quantum mechanics model, where energy levels are called atomic orbitals.
- The intensity of emission is directly proportional to the difference in the two energy levels.
- The lower energy state is denoted by n1, and the higher energy state is denoted by n2.
Frequency and Wavelength Relation
There’s a mathematical relation between the speed of light, frequency, and wavelength which is represented as follows:
c=λv
- where c is the velocity of light
- λ is the wavelength
- v is the frequency
- Further rearranging the equation,
λ=c/v
or, v=c/λ
The above equations indicate that wavelength and frequency are inversely related to each other.
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Hydrogen Spectrum Diagram
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The diagram for hydrogen emission spectrum are as follows:
Hydrogen Spectrum Diagram
Hydrogen Spectrum Wavelength
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Whenever a hydrogen atom absorbs a photon, the electron undergoes an energy level transition from a higher to a lower energy state. When a photon passes through a hydrogen atom, the electron transitions from a higher to a lower energy state, for example, n=3, n=2.
- The spectrum comprises wavelengths that reflect the differences in the quantized energy levels.
- These energy levels exist due to the quantized energy levels of the atoms.
- For example, the line at 656 nm corresponds to the transition n=3 n=2.
Hydrogen Emission Spectrum
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The hydrogen emission spectrum is divided into several spectral series, with wavelengths calculated using the Rydberg formula. The spectral lines are formed by electrons in an atom transitioning between two energy levels.
- The Rydberg formula became crucial in the development of quantum mechanics because it categorized the series.
- In astronomical spectroscopy, spectral series help in identifying the presence of hydrogen and calculate red transitions.
- The Balmer series is the component of the hydrogen emission spectrum.
- It is responsible for an electron's excitation from the second shell to any other shell.
Below is a list of different types of hydrogen emission spectrum:
| Hydrogen Spectrum Series | Data |
|---|---|
| Lyman series | Transition from the first shell to any other shell |
| Balmer series | Transition from the second shell to any other shell |
| Paschen series | Transition from the third shell to any other shell |
| Bracket series | Transition from the fourth shell to any other shell |
| Pfund series | Transition from the fifth shell to any other shell |
Hydrogen Emission Spectrum
Hydrogen Spectrum Series Formula
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A large number of spectral lines are present in the hydrogen spectrum. However, in 1890, Rydberg gave a very simplified theoretical equation for the wavelength of these lines. The equation provides a calculation of the wavenumber v of the lines by the formula:
Here, R is a constant called the Rydberg constant, and its value is equivalent to 109677 cm−1. Also, n1 and n2 are whole numbers and for a particular series, n1 is constant and n2 varies.
- For the Lyman series, n1=1, n2=2,3,4........
- For the Balmer series, n1=2, n2=3,4,5........
- For the Paschen series, n1=3, n2=4,5,6........
- For the Brackett series, n1=4, n2=5,6,7........
- For the Pfund series, n1=5, n2=6,7,8........
For H-like particles, the formula is:
Where Z is the atomic number of the H-like particle.
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Things To Remember
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- Hydrogen spectrum refers to transition of electron from a higher energy level to a lower energy level, the difference in energies between the two levels is emitted as a specific wavelength of radiation.
- The infinity level indicates the maximum amount of energy that an electron can have as a component of a hydrogen atom.
- The hydrogen spectrum lines are: Lyman series, Balmer series, Paschen series, Brackett series, Pfund series.
- The infinity level denotes the point at which the atom is ionised to create a positively charged ion.
- Hydrogenic (Hydrogen like) atoms consist of a nucleus with positive charge ‘+Ze’ and a single electron.
Sample Questions
Ques. What is the wavelength of the light emitted when the electron in a hydrogen atom undergoes transition from the energy level with n = 4 to energy level n = 2 ? What is the colour corresponding to this wavelength ? (Given RH = 109678 cm-1) (2 marks)
Ans. According to Balmer formula,
Ques. Emission transitions in the Paschen series end at orbit n = 3 and start from orbit n and can be represented as v = 3.29 x 1015 (Hz) [1/32 – 1 /n2]. Calculate the value of n if the transition is observed at 1285 nm. Find the region of the spectrum? (3 marks)
The Paschen series lies in the infrared region of the spectrum.
Ques. What transition in the hydrogen spectrum would have the same wavelength as the Balmer transition n = 4 to n = 2 of He+ spectrum? (4 marks)
Ans. For He+ ion, the wave number (v) associated with the Balmer transition, n=4 to n=2 is given by:
By hit and trial method, the equality given by equation (1) is true only when n1=1 and n2=2.
∴The transition for n2=2 to n=1 in hydrogen spectrum would have the same wavelength as Balmer transition n=4 to n=2 of He+ spectrum.
Ques. Name the series of hydrogen spectra which lies in the ultraviolet region. Give an explanation to support your answer? (5 marks)
Ans. The atomic hydrogen emits a line spectrum consisting of various series. In the hydrogen spectrum, the spacing between lines within certain sets of the hydrogen spectrum decreases in regular ways. Each of these sets are called spectral series. Balmer, Lyman, Paschen, brackett, and Pfund series are subsequently found in spectral series of the hydrogen spectrum at different wavelengths.
Lyman series:
1λ=R[112−1n2],where,n=2,3,4...
The Lyman series is in the ultraviolet region.
According to third postulate of Bohr’s model, when an atom makes a transition from the higher energy state with quantum number ‘ni’ to the lower energy state with quantum number nf(nf<ni) , the difference of energy is carried away by a photon of frequency vif such that
hvif=Eni−Enf
Since both nf and ni are integers, this immediately shows that in transitions between different atomic levels, light is radiated in various discrete frequencies. For the hydrogen spectrum, the results of the Bohr’s model suggested the presence of other series spectra for hydrogen atoms corresponding to transitions resulting from nf=1 and ni=2,3,etc.; nf=3&ni=4,5,etc. and so on.
Such series were identified in the course of spectroscopic investigations and are known as the Lyman, Balmer, Paschen, Brackett, and Pfund series. the electronic transitions corresponding to these series shown in the below diagram,
Hence, from the above hydrogen spectrum, the series which lies in the ultraviolet region is the Lyman series.
Ques. Give an account of the spectral series of hydrogen atoms? (5 marks)
Ans. Hydrogen atom has a single electron. Its spectrum consists of a series of spectral lines.
Lyman series: Lyman Series consists of spectral lines corresponding to the transition of an electron from higher energy orbits n = 1 and n2 = 2,3,4… These lines belong to the Ultraviolet region.
Balmer series: Balmer series consists of spectral lines emitted during transitions of electrons from higher energy orbits to the second orbit. n1 = 2 and n2 = 3,4,5… .These lines lie in the visible region.
Paschen series: Paschen series consists of spectral lines emitted when an electron jumps higher energy orbits to the third orbit n1 = 3 and n2 = 4,5,6 … .These lines lie in the infrared region.
Brackett series: Brackett series consists of spectral lines emitted during transitions of electrons from higher energy orbits to fourth orbit. n1 = 4 and n2 = 5,6,7…
Pfund series: Pfund series consists of spectral lines emitted during transition of electrons from higher energy orbits to the fifth orbit. n1 = 5 and n2 = 6,7,8… . These lines lie in the infrared region . The transition from (n1+1) to n1 corresponds to the Ist member or longest wavelength of the series. The transition from (infinity) state to ‘n1’ state corresponds to the last number or series limit or shortest wavelength of the series.
Ques. Determine the ratio of wavelengths of the last line found in the Balmer series and the last line of the Lyman series? (3 marks)
Ans. Given that: 1/λ=Z2R[1/n12−1/n22]
For the last Balmer series: n1 = 2, n2 = ∞ , Z = 1
= 1/λb=R[1/22−1/∞2]
= λb = 4/R
Similarly, For the last Lyman series
= 1/λl = R[1/12−1/∞2]
= λ1 = 1/R
λb/λl = (4/R)/(1/R)
Therefore λb/λl = 4
Ques. Consider an electron in a hydrogen atom excited from the third state to the ground state then calculate the de Broglie wavelength associated with the electron change? (3 marks)
Ans. As we know that for third excited state n2 = 4,
= In case of ground state n1 = 1 and 1/λ=Z2R[1/n12−1/n22]
= 1/λ = R(1/12-1/42)
= 1/λ = 109677 × (15/16)
= λ = 16/(109677 × 15)
= λ = 97 nm
Ques. What is the shortest wavelength of photons emitted in the Brackett series of the hydrogen spectrum and also determines the part of the spectrum it belongs to? [Given Rydberg constant, R = 1.1 × 107 m-1] (3 marks)
Ans. As we know that in bracket series, n1 = 4 and shortest wavelength (n2) = ∞
We know that 1/λ=Z2R[1/n12−1/n22] and Z=1
1/λ = R(1/42-1/∞2)
1/λ = R/16
λ = 16/1.1 × 107
λ = 1454 nm
This implies that the spectrum lies in the Infrared region of the spectrum.
Ques. What is the shortest wavelength limit for the Balmer series of the hydrogen spectrum when the shortest wavelength limit for the Lyman series of the hydrogen spectrum is 913.4 A? (3 marks)
Ans. As we know that: λl for layman series = 913.4 Å
We know that 1/λ=Z2R[1/n12−1/n22] and Z=1
1/913.4 = R[1/12−1/∞2]
For a short limit of wavelength for the Balmer series,
1/λb = R[1/22−1/∞2]λb
=4/R
=4(913.4)
or
λb = 365.36 nm.
Ques. How is hydrogen spectrum formed? (2 marks)
Ans. A hydrogen molecule is first divided into individual hydrogen atoms. An excited electron in a hydrogen atom takes in energy. When an electron returns to its initial condition after making a jump from one energy level to another, it releases energy that creates a hydrogen spectrum.
Ques. What are the two postulates of Bohr's model of the hydrogen atom? (2 marks)
Ans. The two postulates of Bohr’s model of the hydrogen atom are as follows:
- Orbits are the circular paths that revolve around the nucleus in which the electron is revolving.
- The energy of an electron revolving in a hydrogen atom's orbit is not determined by time.
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