On the optimization of Bohrs theory of hydrogen atom

Since the velocity of orbital electrons in atoms is of the order of 106 m/s and comparable with the velocity of electromagnetic wave in free space, its relativistic variation of mass cannot be ignored. The Bohr's theory of hydrogen atom is studied again with and without considering the relativistic variation of mass of orbital electron. When a free proton and an electron combine to form a hydrogen atom, half of the loss of its potential energy is converted into its kinetic energy required to move in a stable orbit surrounding the proton and the remaining half is deposited as relativistic increase of its mass. The orbital electron binds with the proton where the atomic binding energy comes from the energy equivalent of the added mass of the system. This energy is radiated out as electromagnetic waves. It is shown that the energy released during the electronic transition from orbit with quantum number n2 to n1 is equal to the energy equivalent of relativistic variation of mass of the electron. i. e. , ΔE = Δm c² = (mn1 - mn2) c². It gives same value by the difference of total energy of the orbital electron in n1 and n2, ΔE = En2 - En1.