Hydrogen Emission Spectrum

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.