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56 chemistry Each orbital in an atom, therefore, is angular momentum of the electron — a vector defined by a set of values for n, l and m. ln quantity, can have two orientations relative to orbital described by the quantum numbers the chosen axis. These two orientations are n = 2, l = 1, m = 0 is an orbital in the p sub- distinguished by the spin quantum numbers l shell of the second shell. The following chart m s which can take the values of +½ or –½. gives the relation between the subshell and These are called the two spin states of the the number of orbitals associated with it. electron and are normally represented by Value of l 0 1 2 3 4 5 two arrows, ↑ (spin up) and ↓ (spin down). Two electrons that have different m values (one +½ Subshell notation s p d f g h s number of orbitals 1 3 5 7 9 11 and the other –½) are said to have opposite spins. An orbital cannot hold more than two Electron spin ‘s’ : The three quantum electrons and these two electrons should have numbers labelling an atomic orbital can be opposite spins. used equally well to define its energy, shape To sum up, the four quantum numbers and orientation. But all these quantum numbers are not enough to explain the line provide the following information : i) n defines the shell, determines the size spectra observed in the case of multi-electron of the orbital and also to a large extent atoms, that is, some of the lines actually occur the energy of the orbital. in doublets (two lines closely spaced), triplets ii) There are n subshells in the nthshell. l (three lines, closely spaced) etc. This suggests identifies the subshell and determines the presence of a few more energy levels than predicted by the three quantum numbers. the shape of the orbital (see section 2.6.2). There are (2l+1) orbitals of each In 1925, George Uhlenbeck and Samuel type in a subshell, that is, one s orbital Goudsmit proposed the presence of the fourth (l = 0), three p orbitals (l = 1) and five quantum number known as the electron d orbitals (l = 2) per subshell. To some spin quantum number (m ). An electron extent l also determines the energy of s spins around its own axis, much in a similar the orbital in a multi-electron atom. way as earth spins around its own axis while iii) m designates the orientation of the revolving around the sun. In other words, l orbital. For a given value of l, m hls an electron has, besides charge and mass, (2l+1) values, the same as the number intrinsic spin angular quantum number. Spin of orbitals per subshell. It means that Orbit, orbital and its importance Orbit and orbital are not synonymous. An orbit, as proposed by Bohr, is a circular path around the nucleus in which an electron moves. A precise description of this path of the electron is impossible according to Heisenberg uncertainty principle. Bohr orbits, therefore, have no real meaning and their existence can never be demonstrated experimentally. An atomic orbital, on the other hand, is a quantum mechanical concept and refers to the one electron wave function in an atom. It is characterized by three quantum numbers (n, l and ml and its value depends upon the coordinates of the electron.has, by itself, no physical meaning. It is the square of the wave function i.e., |ψ| which has a physical meaning. |ψ| at any point in an atom gives the value of probability density at that point. Probability density (| is the probability per unit volume and the product of |ψ| and a small volume (called a volume element) yields the probability of finding the electron in that 2 volume (the reason for specifying a small volume element is that | varies from one region to another in space but its value can be assumed to be constant within a small volume element). The total probability of finding the electron in a given volume can then be calculated by the sum of all the products of | and the corresponding volume elements. It is thus possible to get the probable distribution of an electron in an orbital. Reprint 2026-27