Putting in the values discussed above into the equation above we get :. Since r = n 2h 2 / 4π 2kmq 1q 2 we can replace this in the above equation to give us:. Deriving Velocity of an Electron in a Stationary State Replacing the values as stated above and putting the mass of an electron as 9.1 x 10 -31 kg we get :-įor the first orbit of the hydrogen atom, n = 1 and Z = 1, we have r = 52.9 pm which is called the Bohr Radius. Since the electrostatic force acts as the centripetal force here we can equate both the equations as:-įrom the Bohr’s Quantization Principle we have :. R is the distance between the protons and the electrons, in this case, the radius of the circular orbit Q 2 is the charge of the protons which is Z x 1.6 x 10 -19 C Q 1 is the charge of the electron which is 1.6 x 10 -19 C The electrostatic force between the electron and the protons comes out to be:. Z represents the atomic number of the atom. There are Z number of protons in an atom. In a hydrogen atom or a hydrogen-like atom the centripetal force is maintained by the electrostatic force of interaction between the electron and the protons. This centripetal force can be stated in the form of an equation as, Stationary States Of Bohr’s Atomic Model ( Source) Deriving Radius of a Stationary Stateįor a body moving in a uniform circular motion, a centripetal force acts on it maintaining the circular motion. Therefore we have derived Bohr’s Quantization Principle, and have defined the stationary state. L is the angular momentum of the electron the circular path The de-Broglie Equation states that :-įor an electron with a de-Broglie wavelength of λ, for it to maintain a sustained wave the wavelength should be equal to the circumference of the circular path. Bohr’s Quantization Principle defines these stationary states as circular paths on which the angular momentum of the electron is an integral multiple of h/2π.įormulas for Bohr’s Atomic Model Deriving Bohr’s Quantization Principleīohr’s Quantization Principle can be derived using the de-Broglie Equation.The energy of the electron changes only when it makes transitions from the energy level of one stationary state to the energy level of another stationary state.So, these are called the stable orbits and they have quantised energy. An electron revolving in these fixed circular path doesn’t radiate energy as per Maxwell’s laws and maintains a constant energy value. The electron revolves around fixed circular paths of fixed radius and energy called stationary states.The singular proton of the hydrogen atom or the protons and neutrons of the hydrogen-like species(ex- He +, Li 2+, etc.) are present in the centre of the atom, in a positively charged nucleus.Hydrogen Bohr model was based on some assumptions which are listed below: Deriving Energy of an Electron in a Stationary Stateīohr’s Atomic Model was for the hydrogen atom and hydrogen-like species(species with only one electron).Deriving Velocity of an Electron in a Stationary State.As a result, Rutherford’s Atomic Model doesn’t work. Atoms don’t form and simultaneously blow up. The electron spirals moving closer to the nucleus eventually would collapse into it in what calculations suggest a time of 10 -8 s.īut life still lives on. Thus, negatively charged electrons would emit energy as they revolve around the nucleus, with its orbit decreasing with time. Maxwell’s Laws of Electrodynamics suggest that a charged particle moving in a circular orbit releases energy in the form of electromagnetic radiation. It was like our solar system, with planets revolving around the sun, a beautiful symmetry that sadly wasn’t feasible. The Rutherford Atomic Model placed the protons and neutrons inside a small structure called the ‘nucleus’ with the electrons revolving around the nucleus in circular orbits. Discovery of the proton, electron, and neutron, made us wonder, what does the atom actually look like? With his classic, Alpha Ray Scattering Experiment Rutherford was able to suggest a possible model for the atom. Research, experiments, and theory into the atomic structure have resulted in much understanding of the stuff that makes us.ĭalton’s Atomic Theory, which stated that atoms are indivisible was shattered with the discovery of subatomic particles, which make up the atom. Let us look at a bit of history and then get into the details of this model. It was basically a modified version of Rutherford’s Atomic Model wherein Bohr explained that electrons move in fixed orbitals (shells) and not anywhere in between and he also explained that each orbit (shell) has a fixed energy level. Bohr’s Atomic Model was introduced by Niels Bohr in 1915.
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