Sunday, February 1, 2015

Bohr's Line spectrum of hydrogen atom

When an electron jumps from higher orbit to lower orbit, the difference in the energies of the orbits is released in the form of photon with a certain frequency. By writing the equations for their energies and by subtracting them we can derive the equation for the frequency and the wavelength as shown below. Here we will get a constant called as Ridberg constant.

Emission spectrum of hydrogen atom

Electron in a hydrogen atom can be navigated straight for a very small time. It is not stable there therefore it always preferred to jump into the lower orbits. Once if it is in the lower orbit it will have less potential energy and it will be more stable. Therefore electrons always tended to jump from higher orbits to lower orbits whenever there is a vacancy. The emitted energy in this process is in the form of photons. This photon will have a certain frequency and the spectrum of all these frequencies could be called as emission spectrum.

Lyman series

Depending on electron jumping from which orbit to which orbit, the emitted energies and their corresponding frequencies are different. If the electronic jumping into the ground state, the corresponding spectral line is called Lyman series. In this case, electrons from different higher orbits are always going to jump into the ground state. We can calculate the corresponding wavelength and frequencies and they are maximum and minimum values as shown below. This region in the ultraviolet region which is in invisible region.

Balmer series

If the electrons from the different orbits jump into the second orbit, the corresponding emitted energies in the frequencies are called Balmer series. These corresponding wavelengths and frequencies are in the visible region. In fact this is the only frequencies that are visible in the bourse atomic model.

We can derive the corresponding wavelength and frequencies for this region as shown below.

Passion series and Bracket series

If the electron is jumping into the third orbit the corresponding frequencies emitted are represented as Passion series. If the electron jumps into the fourth orbit from different orbits the corresponding frequencies set is called Bracket series. Their corresponding wavelengths and energies are as shown below. The respective spectrum diagram is also shown.

We can calculate the number of the spectral lines possible between two specified orbits as shown below.

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