Velocity and Time period of electron in Bohr orbit

Velocity of the electron in the orbit

We know that according to Bohr’s atomic model, electrons revolve in specified orbits. These orbits are called stationery orbits. When the electron is in that orbit, it neither loose energy nor gain that energy. The electron in this orbit will have a specific velocity and we can derive the equation for the velocity.

According to second postulate the angular momentum of the electron is integral multiples of a constant. This number which is an integral multiple is actually called as principal quantum number. Taking this concept into consideration we can write the equation for the velocity of the electron in that terms. It can be mathematically proved that velocity of the electron in any orbit is independent of mass of electron. It is directly proportional to atomic number and is inversely proportional to principal quantum number. We can calculate the velocity of the electron in the first orbit by writing atomic number as well as the principal quantum member equal to 1. The expression for the velocity is derived as shown below.

Time period of the electron in the orbit

As the electron is revolving the in a circular path, it take specific time to complete one rotation. This specific time is called time period. We can derive the equation for the time period by writing a small relation between linear velocity and the angular velocity of the electron. The derivation is as shown below. It is proved that time period of the electron is directly proportional to cube of the principal quantum number and inversely proportional to Squire of the atomic number.