IIT JEE and NEET Physics @ Venkats Academy IIT-JEE and NEET Physics

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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Potential and Kinetic energy of electron in the orbit

We know that the electron is revolving in a specified orbit. We also know that these orbits are called stationery orbits. When the electron is in the stationary orbit, it neither loose the energy nor gain the energy. Hence it has a fixed energy. This energy is both in the forms of potential energy and kinetic energy. We can derive the equations for both potential and kinetic energies as shown below. By adding potential and kinetic energies we can get the total energy of the electron. It is the observed by the results that the total energy and the potential energy are negative values. It is a symbolic way of expressing that the electron is associated with the nucleus.

It is also noticed that potential energy is twice the magnitude of total energy. It is observed that the magnitude of total energy and the kinetic energy are equal.

The expression for the kinetic energy is done taking the basic equation of kinetic energy and substituting the value of the velocity of the electron that is derived. Again potential energy is defined basing on the very definition of electrostatic potential energy. By adding both these energies we got total energy.

It is observed that all these energies are directly proportional to Squire of the atomic number and inversely proportional to Squire of principal quantum number.

Energy levels of electron in different orbits

We know that electrons revolve is in different orbits around the nucleus. Basing on the orbit each electron will have different energy. As the number of the orbit is increasing the total energy of the electron also increases and at the infinite orbit it’ll becomes zero. We can express the total energy of any of the electron in terms of the basic energy of the electron in the ground state which is equal to -13.6 electron volt.

Energy of the electron in any other orbit is this numerical value divided by Squire of the principal quantum number. Basing on the above result, we can write energies of different orbits not only for the hydrogen atom, even for the hydrogen like attempts as shown below.

Problem and solution

An electron in a hydrogen atom makes the transition from one orbit to another orbit. Assume that the Bohr atomic model is valid. It is given that the time period of the electron in the initial state is eight times of the final state. What are the possible values of principal quantum numbers?

We have proved that the time period of an electron in a given orbit is directly proportional to cube of principal quantum number. Taking this into consideration we can derive a direct relation between principal quantum numbers. As we know that the principal quantum number is not a fractional value, basing on that and the relation we can write different sets of values of principal quantum numbers for the above problem as shown below.