State the postulates of Bohr's theory of hydrogen atom. Write the necessary equations.

Explanation

Niels Bohr combined Rutherford's nuclear atom with the quantization and photon concepts to develop, in 1913, a fairly successful model of the hydrogen atom on the basis of the following postulates :
Postulate 1: In a hydrogen atom, the electron revolves with a constant speed in a circular orbit around the nucleus, the necessary centripental force required for uniform circular motion being the Voulomb force of attraction of the positive nuclear charge on the negatively charged electron.
Let m be the mass and -e the charge on the electron. The charge on the hydrogen nucleus is `+e`. If the electron moves with a speed v along the circular orbit of radius r, centripetal force=electrostatic force
`:. (mv^(2))/(r )=(1)/(4piepsilon_(@))(e^(2))/(r^(2))`
where `epsilon_(@)` is the permittivity of free space.
Postulate 2 : The electron can revolve without radiating energy only in certain orbits in which the angular momentum of the orbiting electron is equal to an integral multiple of `h//2pi`, where h is Planck's constant.
Such orbits are called allowed orbits, or stationary energy states. Thus, angular momentum L=mvr is quantized :
`L=mvr=(nh)/(2pi)`
where n=1,2,3,...., etc. The interger n is called the principal quantum number and it denotes the number of the orbit.
Postulate 3 : Energy is radiated by the electron only when it jumps from a higher energy state to a lower energy state. The energy of the quantum of radiation emitted is equal to the energy difference of the two states.
The radiation of energy is in the form of a photon of energy hv, where v is the frequency of radiation. If `E_(i)` and `E_(f)` are the energies of the electron in the initial(higher) energy state and final (lower) energy state,
`E_(i)-E_(f)=hv`