Hydrogen bohr model11/2/2022 ![]() 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.
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