Physical Models

Physical Models, Experimental Observations

Rutherford Model: Rutherford bombarded a thin gold foil with Alpha particles (He++) having atomic mass 4. Many particles went through un-deflected and some deflected by large angle. He concluded that atoms have large void spaces and a central mass (nucleus) about (1/10000) of the size of the atom. This nucleus is surrounded by extremely light electrons, which are revolving around it just like the planets revolve around the sun. The centripetal force (mv2/r) is balanced by electrostatic attraction between the nucleus and the electron (ze2/4𝜇πεo /r2).

When it was verified on Hydrogen atom, some drawbacks appeared in this model. First was that although this model permits the electrons to have any value of energy, experiments confirm that the electrons actually have specific or discrete values of energy. Also, Maxwell equations suggest that moving charges radiate energy. Thus revolving electrons would lose energy and the reduction in the kinetic energy would make tem fall upon the nucleus!

Bohr Model: Neils Bohr proposed a model for Hydrogen atom retaining the essentials of earlier model but modifying the behavior of the electron, restricting the path of electrons to widely separated orbits called stationary orbits. These permissible orbits have angular momentum = (n.h/2π), where n (an integer) is called quantum number. Bohr postulated that an atom radiates energy only when an electron jumps from orbit of higher energy to orbit of lower energy [E1–E2 = hν]. Let us study the spectral lines {Lyman, Balmer, Paschen, Brackett and Pfund series} emitted by a hydrogen atom.

But Bohr’s model failed to explain the spectra of atoms bigger than hydrogen; arrangement of electrons in an atom, fine lines observed in the spectral lines, rules fortransition of electrons from one to other orbit, quantitative study of chemical bonding, splitting of spectral lines by the application of electric field (Zeeman Effect) or magnetic fields (Stark Effect).

Sommerfeld’s correction of Bohr Model: He proposed that: a) the path of the electrons around the nucleus is elliptical, and b) variation in the velocity of the electrons along the elliptical path causes relativistic variation in the mass of the electron. Thus a moving electron has two momenta: along the radius vector called radial momentum and perpendicular to radius vector called the angular momentum. The principal quantum number n = (nr + nΦ), where nr is radial quantum number and nΦ is the angular quantum number. For n = 2, the values that nΦ can take are 1 and 2. And for n =3, the values that nΦ can take are 1, 2 and 3. Thus if an electron falls from third to second orbit, there are

sixtransitionspossible.Thesecanbe: 3322,3321,3222,3221,3122,and 31  22. (givng rise to six lines within the Hα spectrum line) Even with the above modification, the distribution and arrangement of electrons in an atom could not be fully explained. It also failed to explain the intensity of spectral lines. Neither could it explain the Zeeman or Stark Effect. Vector Atom Model: It added two postulates: the spinning of electron and the spatial quantization (the direction or orientation) of the orbits, adding a new quantum number called magnetic orbital quantum number. Thus all the quantum numbers are: principal quantum number, orbital quantum number, magnetic orbital quantum number and spin quantum number. Pauli’s exclusion principle states that no two electrons can exist in the same quantum state. This explained the electronic configuration of the atom and led to the formation of the periodic table of elements (which divides the atoms in to light metals, transition metals, non-metals, and soft metals. Wave Mechanical Concept of Atom: deBroglie proposed that particles such as the electrons possess many properties of waves. He theoretically concluded that particles of mass m moving with a velocity v would behave as a wave, having a wavelength λ = h/mv. Thus electron revolved around the nucleus in any permissible orbit.