What is Hydrogen Emission Spectrum Balmer Series and Rydberg Equation
As any other atom, the hydrogen atom also has electrons that revolve around a nucleus. Electrons experience several quantum states due to the electromagnetic force between proton and electron. Neil Bohr’s model helps us visualise these quantum states as electrons orbit around the nucleus in different paths. But later, with the introduction of quantum mechanics, this theory went through modification. This theory states that electrons do not occupy an orbit instead of an orbital path. But the energy level theory remains the same. Now we will further look at what is Hydrogen emission spectrum? And the movements of electrons in the different energy levels inside an atom.
What is Hydrogen Emission Spectrum?
To understand what is Hydrogen emission spectrum, we will discuss an experiment. Consider a slim tube containing pressure gaseous hydrogen at low pressures. Next, we will attach an electrode at both ends of the container. Now if we pass high voltage electricity through the electrode than we can observe a pink glow (bright) in the tube. We know that prism splits the light passing through it via diffraction. The visible light is a fraction of the hydrogen emission spectrum. Our eyes are not capable of detecting most of the range due to the light being ultraviolet. The leading cause of the line emission spectrum of the hydrogen is electron passing from high energy state to a low energy state.
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When we observe the line Emission Spectrum of hydrogen than we see that there is way more than meets the eye. The line emission spectrum of hydrogen allows us to watch the infrared and ultraviolet emissions from the spectrum as they are not visible to the naked eye. Looking closely at the above image of the spectrum, we see various hydrogen emission spectrum wavelengths. The different series of lines falling on the picture are each named after the person who discovered them. In the below diagram we can see the three of these series laymen, Balmer, and Paschen series.
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Relation Between Frequency and Wavelength
The representation of the hydrogen emission spectrum using a series of lines is one way to go. But we can also use wavelength to represent the emission spectrum. The speed of light, wavelength, and frequency have a mathematical relation between them. However, this relation leads to the formation of two different views of the spectrum. One is when we use frequency for representation, and another is the wavelength. Now let us discuss this relationship between the speed of light ( c ), wavelength(), and frequency().
\[c = \lambda v\]
Further rearranging the equation
\[\lambda = \frac{c}{v}\]
Or,
\[v = \frac{c}{\lambda}\]
From the above equations, we can deduce that wavelength and frequency have an inverse relationship.
What is Hydrogen Emission Spectrum Series?
Since now we know how to observe emission spectrum through a series of lines? We shall discuss a variety of Hydrogen emission spectrum series and their forefathers. Starting with the series that is visible to the naked eye. To relate the energy shells and wavenumber of lines of the spectrum, Balmer gave a formula in 1855.
\[\overline{v} = 109677(\frac{1}{2^{2}} - \frac{1}{n^{2}})\]
Where v is the wavenumber, n is the energy shell, and 109677 is known as rydberg’s constant.
This series is known as Balmer series of the hydrogen emission spectrum series. Balmer series is also the only series in the visible spectrum. The Balmer series of the emission spectrum of hydrogen mainly enables electrons to excite and move from the second shell to another shell. Likewise, there are various other transition names for the movement of orbit. The leading five transition names and their discoverers are:
Lyman Series: This series involves the transition of an excited electron from the first shell to any other shell.
Balmer Series: This series consists of the change of an excited electron from the second shell to any different orbit.
Paschen Series: This series involves the change of an excited electron from the third shell to any other shell.
Bracket Series: This series consists of the transition of an excited electron from the fourth shell to any other orbit.
Pfund Series: This series consists of the transition of an excited electron from the fifth shell to any other orbit.
A Swedish scientist called Rydberg postulated a formula specifically to calculate the hydrogen spectral line emissions ( due to transition of electron between orbits). Let us derive and understand his formula. The formula is as follows:
\[\overline{v} = 109677(\frac{1}{2^{2}} - \frac{1}{n^{2}})\]
Where,
v is the wavenumber
The number 109677 is called Rydberg’s hydrogen constant.
N1 and n2 are the whole numbers
n1= 1, 2, 3, ....
n2= ( n1+1 ), i.e. n2, should always be greater than n1.
To simplify n1 and n2 are the energy levels on both ends of a spectral line. For instance, we can fix the energy levels for various series. For layman’s series, n1 would be one because it requires only first shell to produce spectral lines. Similarly, for Balmer series n1 would be 2, for Paschen series n1 would be three, for Bracket series n1 would be four, and for Pfund series, n1 would be five.
FAQs on Hydrogen Emission Spectrum and Line Series Explained
1. What is the hydrogen emission spectrum?
The hydrogen emission spectrum is the set of discrete wavelengths of light emitted when excited hydrogen atoms return to lower energy levels. When an electron in a hydrogen atom falls from a higher energy level (n2) to a lower one (n1), it emits light of a specific wavelength, producing bright lines on a dark background. These lines form a line spectrum rather than a continuous spectrum because hydrogen has quantized energy levels.
2. Why does hydrogen show a line spectrum instead of a continuous spectrum?
Hydrogen shows a line spectrum because its electrons can occupy only specific quantized energy levels. Each spectral line corresponds to a transition between two fixed energy levels.
- Electrons absorb energy and jump to higher levels.
- When they return to lower levels, they emit photons of exact energy.
- The photon energy is given by E = hν, where h is Planck’s constant and ν is frequency.
3. What are the different series in the hydrogen emission spectrum?
The hydrogen emission spectrum consists of several spectral series, each corresponding to electron transitions ending at a specific energy level.
- Lyman series: transitions to n = 1 (ultraviolet region).
- Balmer series: transitions to n = 2 (visible region).
- Paschen series: transitions to n = 3 (infrared region).
- Brackett series: transitions to n = 4 (infrared region).
- Pfund series: transitions to n = 5 (infrared region).
4. What is the Rydberg formula for the hydrogen emission spectrum?
The Rydberg formula for hydrogen is 1/λ = RH (1/n12 − 1/n22), where n2 > n1. Here, λ is the wavelength, RH = 1.097 × 107 m−1 is the Rydberg constant, n1 is the lower energy level, and n2 is the higher energy level. This equation accurately predicts the wavelengths of all lines in the hydrogen emission spectrum.
5. How is the Balmer series formed in the hydrogen emission spectrum?
The Balmer series is formed when electrons in hydrogen fall from higher levels (n ≥ 3) to n = 2. These transitions produce visible light lines, such as:
- n = 3 → 2 (Hα line, red light)
- n = 4 → 2 (Hβ line)
- n = 5 → 2 (Hγ line)
6. How do you calculate the wavelength of a line in the hydrogen emission spectrum?
You calculate the wavelength using the Rydberg formula: 1/λ = RH (1/n12 − 1/n22).
- Step 1: Identify n1 (lower level) and n2 (higher level).
- Step 2: Substitute into the equation.
- Step 3: Solve for λ.
1/λ = (1.097 × 107)(1/22 − 1/32)
This gives λ ≈ 656 nm, which corresponds to red light.
7. What is the difference between emission and absorption spectra of hydrogen?
The emission spectrum shows bright lines produced when electrons fall to lower energy levels, while the absorption spectrum shows dark lines where light has been absorbed.
- Emission: excited atoms emit specific wavelengths.
- Absorption: ground-state atoms absorb the same specific wavelengths.
- Both spectra involve identical energy level differences.
8. How did the hydrogen emission spectrum support Bohr’s atomic model?
The hydrogen emission spectrum supported Bohr’s atomic model by confirming that electrons occupy quantized energy levels. Bohr proposed that:
- Electrons move in fixed circular orbits.
- Each orbit has a specific energy.
- Light is emitted when an electron jumps between orbits.
9. Why is the Lyman series found in the ultraviolet region?
The Lyman series lies in the ultraviolet region because it involves transitions to the lowest energy level, n = 1, which release high-energy photons. Since energy and wavelength are inversely related (E = hc/λ), large energy differences produce short wavelengths. Ultraviolet light has shorter wavelengths than visible light, so transitions ending at n = 1 fall in the UV region.
10. What is the significance of the hydrogen emission spectrum in chemistry?
The hydrogen emission spectrum is significant because it provides direct evidence for quantized energy levels and forms the basis of modern atomic theory.
- It led to the development of Bohr’s model of the atom.
- It helps determine electronic transitions and atomic structure.
- It is used in spectroscopy to identify elements in stars and laboratories.
