Knowing More On Hydrogen Spectral Series

A hydrogen spectrum is defined as the spectral lines of radiation emitted from a hydrogen atom. The spectral lines fall between the ultraviolet and infrared regions of the electromagnetic spectrum and are a result of the electronic transitions from one energy level to another. These lines are divided into six series and named after the people who discovered them and are characteristic of the hydrogen atom. The hydrogen spectral series of transitions and emissions include the Lyman series, Balmer series, Paschen series, Brackett series, Pfund series, and Humphery series. The Lyman and Blamer series fall in the ultraviolet and visible spectrum region, respectively, while the Paschen, Brackett, Pfund, and Humphery series fall in the infrared spectrum region. 

Internal Structure of the Atom

In 1913, a Danish scientist, Neils Bohr, suggested the hydrogen atom’s model structure. He gave the following postulates:

• The electron of the hydrogen atom moves around the nucleus in certain specific circular orbits, also called energy levels and the centrifugal force caused by this motion balances the electrostatic attraction between the electrons and the nucleus. Thus, the electrons move in such orbits without emitting radiation or losing energy. He called these orbits the ground states of the electrons.
• When the electron jumps from one orbit to another, light energy is emitted. These jumps are done in a quantum manner, and the energy radiated is in the form of a single photon of light given by the formula:

E2–E1=∆E=hf

 E2 and E1 are the energy levels of the upper and lower states, respectively,

h is the Planck’s constant, 6.626×10-34 Js,

and f is the frequency of the emitted light

Thus, Bohr’s model accounted for the presence of line spectrum emissions of the hydrogen atom.

• The electron’s angular momentum was quantised, i.e., are discrete values, and the magnitude for the electron is given by: 

mevnrn=nh2 

 me is the mass of the electron,

 vn is the velocity,

 rn is the radius of the orbit,

And n represents the value of the orbit.

For Bohr’s model of the internal structure of the hydrogen atom, the proton is said to be at rest, but the electron moves in a circular orbit of the radius rn with speed vn. Therefore, giving the atomic diameter as 10-10m  which is similar to J.J Thompson’s model of an atom. 

Origin Of The Hydrogen Emission Spectrum

When the hydrogen’s electron is not excited, it is in its ground state, which is closest to the nucleus. But when energy is supplied to the atom, the electron becomes excited and jumps to a higher energy level or could get displaced from the atom. The electron could also lose energy and fall down to a lower level. This process gives rise to the spectral lines in the hydrogen emission spectrum.

Series Of The Hydrogen Emission Spectrum

LYMAN SERIES

When an electron falls from any of the higher stationary energy levels to the first energy level, the spectral lines fall in the Lyman series. For the Lyman series, n1=1. Using the Bohr’s equation:

1=RH(1n12–1n22)

where RH, is the Rydberg constant which has the value 1.09737×107m-1

is the wavelength of light

n1 and n2 are the energy levels at either end of the jump that produces a spectral line, with n1 being the final energy level and n2 being the initial energy level.

It should be noted that n1 and n2 are integers with n2 being greater than n1

Substituting n1=1 in the equation, we have: 

1=RH(112–1n22)

n2=2,3,4,5,6,7, _ _ _ _

BALMER SERIES

When an electron falls from any of the higher stationary energy levels to the second energy level, the spectral lines fall in the Balmer Series. For the Balmer series, n1=2. Using the Bohr’s equation:

1=RH(122–1n22)

n2=3,4,5,6,7, _ _ _ _

PASCHEN SERIES 

When an electron falls from any higher stationary energy levels to the third energy level, the spectral lines fall in the Paschen Series. For the Paschen series, n1=3. Using the Bohr’s equation:

1=RH(132–1n22)

n2=4,5,6,7, _ _ _ _

BRACKETT SERIES

When an electron falls from any of the higher stationary energy levels to the fourth energy level, the spectral lines fall in the Brackett Series. For the Brackett series, n1=4. Using the Bohr’s equation:

1=RH(142–1n22)

n2=5,6,7, _ _ _ _

PFUND SERIES 

When an electron falls from any of the higher stationary energy levels to the fifth energy level, the spectral lines fall in the Pfund Series. For the Pfund series, n1=5. Using the Bohr’s equation:

1=RH(152–1n22)

n2=6, 7, _ _ _ _

HUMPHERY SERIES

When an electron falls from any of the higher stationary energy levels to the sixth energy level, the spectral lines fall in the Humphery Series. For the Humphery series, n1=6. Using the Bohr’s equation:

1=RH(162–1n22)

n2=7, _ _ _ _

The formulae given can be used to calculate the wavelengths of the spectral lines in the hydrogen emission spectrum.

To calculate the frequency of each of the spectral lines, a modified version of the formula can be used:

v=c

=c × 1

If 1=RH(1n12–1n22)

v=c × RH(1n12–1n22)

Where v is the frequency,

and c is the velocity of radiation.

To calculate the wavenumbers of each of the spectral lines, the equation is given as follows:

v=RHZ2(1n12–1n22)

Z represents the atomic number.

CONCLUSION

The emission spectrum of hydrogen has the simplest line spectrum among all the elements and covers a wide range of wavelengths from the ultraviolet to the infrared. The spectral series of transitions in the hydrogen emission spectrum are named after their discoverers. Amongst all the series, the Balmer series was the easiest to study because a number of its spectral lines fall in the visible range of the electromagnetic spectrum.