Banha University

Solution
Bohr model: the hydrogen atom consists of a positively charged nucleus
containing a proton and an orbiting electron.
Bohr postulates:
1. The electron moves in stable circular orbits around the proton under the influence
of the electric force of attraction
2. The allowed orbits are those for which the electron’s orbital angular momentum
about the nucleus is quantized and equal to an integral multiple of ħ: mvr = nħ
where m is the electron mass, v is the electron’s speed in its orbit.
3. The atom emits radiation when the electron makes a transition from a
more energetic initial stationary state to a lower-energy stationary state. The
frequency of the emitted radiation is hf = Ei – Ef
where Ei is the energy of the initial state, Ef is the energy of the final state,
and Ei > Ef.
The radius of the orbits:
The electric force exerted on the electron must equal the product of its mass and its
centripetal acceleration:
Using Bohr’s postulate: mvr = nħ
The energy of the electron
The kinetic energy of the electron
Substituting for the radius of the orbits, then then the total energy