p d f g h number of orbitals Electron spin ‘s’ : The three quantum numbers labelling an atomic orbital can be used equally well to define its energy, shape and orientation. But all these quantum numbers are not enough to explain the line spectra observed in the case of multi-electron atoms, that is, some of the lines actually occur in doublets (two lines closely spaced), triplets (three lines, closely spaced) etc. This suggests the presence of a few more energy levels than predicted by the three quantum numbers. In , George Uhlenbeck and Samuel Goudsmit proposed the presence of the fourth quantum number known as the electron spin quantum number ( m s ).
An electron spins around its own axis, much in a similar way as earth spins around its own axis while revolving around the sun. In other words, an electron has, besides charge and mass, intrinsic spin angular quantum number. Spin angular momentum of the electron — a vector quantity, can have two orientations relative to the chosen axis. These two orientations are distinguished by the spin quantum numbers m s which can take the values of +½ or –½.
These are called the two spin states of the electron and are normally represented by two arrows, ↑ (spin up) and ↓ (spin down). Two elec trons that have different m s values (one +½ and the other –½) are said to have opposite spins. An orbital cannot hold more than two electrons and these two electrons should have opposite spins. To sum up, the four quantum numbers provide the following information : i) n defines the shell, determines the size of the orbital and also to a large extent the energy of the orbital.
ii) There are n subshells in the n th shell. l identifies the subshell and determines the shape of the orbital (see section . . ).
There are ( l + ) orbitals of each type in a subshell, that is, one s orbital ( l = ), three p orbitals ( l = ) and five d orbitals