Excitation Energy

Spectral series refers to a collection of wavelengths whose arrangement takes place in sequential order. These wavelengths are in the form of lines. Calculation of the spectral series is possible by making use of the Rydberg formula. Hydrogen is one of the most studied elements when it comes to spectral series. The excitation energy of hydrogen atoms is an integral part of its spectral series.  Keep on reading to learn all about the excitation energy of hydrogen atoms in spectral series. 

Understanding excitation energy of hydrogen atom:

The first thing we should focus on is the basics of the excitation energy of hydrogen atoms. Excitation refers to the addition of a discrete amount of energy to a molecule, atom, or nucleus. This energy is also known as excitation energy.  Excitation energy brings about an alteration from the ground state to the excited state. The ground state refers to a condition of the lowest energy. On the other hand, the excited state simply represents higher energy.

In nuclear, atomic, and molecular systems, there is not a continuous distribution of the excited states.  These systems only have certain discrete energy values. Therefore, absorption of excitation energy can take place only in correspondingly discrete amounts.

In order to excite a hydrogen atom, the energy needed that must be given to it is as follows:

 E2 – E1 = -3.4 + 13.6 = 10.2 eV. 

Therefore, the first excitation energy of hydrogen atoms comes to be 10.2 eV.

Types of spectral series of hydrogen atoms:

To properly analyse the excitation energy of hydrogen atoms, one must have knowledge of the various types of spectral series. In total, there are four types of spectral series of the hydrogen atom that have been explained below:

Lyman series:

When there is jumping of the electron from an outer orbit to the first orbit, there is an emission of spectral lines in the spectrum’s ultraviolet region. This is how a Lyman series is formed. 

Here, n1 = 1, n2 = 2,3,4,……

The expression of the Lyman series’ wave number is as follows:

v = R(1- (1/n22) )

Balmer series:

When there is jumping of the electron from an outer orbit to the second orbit, the result is the Balmer series. The wavelength of all the lines of this series in hydrogen would be in the visible region. 

Here n1=2, n2 = 3,4,5,…..

The expression of the Balmer series’ wave number is as follows:

v = R( 1/22 – 1/n22 ) = R( 1/4  – 1/n22 )

 Paschen series:

This series involves all wavelengths whose emission takes place when the electron jumps from the outermost orbit to the third orbit. The Paschen series can be found in the infrared region.

Here n2 = 4,5,6,….. and n1 = 3. 

The expression of the Paschen series’ wave number is as follows:

v = R( 1/32 – 1/n22 ) = R( 1/9  – 1/n22 )

Brackett series:

You will get this series by the transition of the electron from n2 = 5, 6… to n1 = 4. The Brackett series is in the infrared region. 

The expression of the Brackett series’ wave number is as follows:

v = R( 1/42 – 1/n22 ) = R( 1/16  – 1/n22 )

Pfund series:

You will get the lines of the series when there is jumping of the electron from any state n2 = 6, 7… to n1=5. Similar to the Paschen series and Brackett series, this series too is in the infrared region. 

The expression of the Pfund series’ wave number is as follows:

v = R( 1/52 – 1/n22 ) = R( 1/25  – 1/n22 )

Energy level excitation 

The expression of the energy of the electron in the hydrogen atom’s nth orbit is as follows,

En = -13.6 /n2   eV

Energy whose association is with the hydrogen atom’s first orbit can be expressed as:

E1 = -13.6 /12   = -13.6  eV

This is the hydrogen atom’s ground state energy. Furthermore, the expression of the energy whose association is with the second orbit is as follows,

E2 = -13.6 /22   = -3.4  eV

This is the hydrogen atom’s first excited state energy. Moreover, the expression of the energy of third, fourth, and fifth excited states of the hydrogen atom is as follows:

 E3 = -1.51 eV

E4 = -0.85 eV

E5 = -0.54eV …

Also, if n =infinity ∞, then we shall have Einf = -13.6 /2  = 0

As we can see from above, the energy whose association is with a state becomes less negative. Moreover, it keeps on approaching closer and closer to the maximum value zero such that it corresponds to

Conclusion

Spectral series refers to a collection of wavelengths whose arrangement is in sequential order. These wavelengths can be observed in the form of lines. Excitation refers to an addition of a discrete amount of energy that brings about an alteration from the ground state to the excited state. Furthermore, E2 – E1 = -3.4 + 13.6 = 10.2 eV is the hydrogen atom’s first excitation energy. After learning the excitation energy of hydrogen atoms, move on to the various types of spectral series of the hydrogen atom. These are of four types- Lyman series, Balmer series, Paschen series, Brackett series, and Pfund series. Finally, try to understand the excitation energy of hydrogen atoms with the help of energy levels.