Sunday, February 1, 2015

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.




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