O RBIT VS STATE ( ORBITAL PICTURE ) OF ELECTRON IN ATOM We are introduced to the Bohr Model of atom one time or the other in the course of physics. This model has its place in the history of quantum mechanics and particularly in explaining the structure of an atom. It has become a milestone since Bohr introduced the revolutionary idea of definite energy orbits for the electrons, contrary to the classical picture requiring an accelerating particle to radiate. Bohr also introduced the idea of quantisation of angular momentum of electrons moving in definite orbits.
Thus it was a semi-classical picture of the structure of atom. Now with the development of quantum mechanics, we have a better understanding of the structure of atom. Solutions of the Schrödinger wave equation assign a wave-like description to the electrons bound in an atom due to attractive forces of the protons. An orbit of the electron in the Bohr model is the circular path of motion of an electron around the nucleus.
But according to quantum mechanics, we cannot associate a definite path with the motion of the electrons in an atom. We can only talk about the probability of finding an electron in a certain region of space around the nucleus. This probability can be inferred from the one-electron wave function called the orbital . This function depends only on the coordinates of the electron.
It is therefore essential that we understand the subtle differences that exist in the two models: Bohr model is valid for only one-electron atoms/ions; an energy value, assigned to each orbit, depends on the principal quantum number n in this model . We know that energy associated with a stationary state of an electron depends on n only, for one-electron atoms/ions. For a multi-electron atom/ion, this is not true. The solution of the Schrödinger wave equation, obtained for hydrogen-like atoms/ ions, called the wave function, gives information about the probability of finding an electron in various regions around the nucleus.
This orbital has no resemblance whatsoever with the orbit defined for an electron in the Bohr model. Example . A kg satellite circles earth once every h in an orbit having a radius of km. Assuming that Bohr’s angular momentum postulate applies to satellites just as it does to an electron in the hydrogen atom, find the quantum number of the orbit of the satellite.
Solution From Eq. ( . ), we have m v n r n = nh/