2 ATOMIC ORBITAL THEORY electrons are placed in orbitals,the energy of the orbitals(and hence the energy of the electrons in them)is affected so that orbitals with the same principal quantum number n may vary in energy. Example.An electron in an orbital with a principal quantum number of n=2 can take onI values of 0 and 1,corresponding to 2s and 2p orbitals,respectively.Although these orbitals have the same principal quantum number and,therefore,the same energy when calculated for the single electron hydrogen atom,for the many-electron whe re e ctron ractions become important,the 2p orbitals ar 1.27 MAGNETIC QUANTUM NUMBER This is the quantum number having values of the azimuthal quantum number from +to-/that determines the orientation in space of the orbital angular momentum; it is represented by m Example.When n=2 and I=1 (the p orbitals).m may thus have values of +1.0. -1,corresponding to three 2p orbitals (see Sect.1.35).When n=3 and I=2,m,has the values of +2,+1,0,-1,-2 that describe the five 3d orbitals (see Sect.1.36). 1.28 DEGENERATE ORBITALS Orbitals having equal energies,for example,the three 2p orbitals. 1.29 ELECTRON SPIN QUANTUM NUMBER m, ntum of the electron due to the fac that the ele on its s spinning:it is usually designated by m,and may only have the value of 1/2 or-1/2 1.30 s ORBITALS Spherically symmetrical orbitals:that is,is a function of R(r)only.For s orbitals, 1=0 and,therefore,electrons in such orbitals have an orbital magnetic quantum number m equal to zero. 1.31 1s ORBITAL The lowest-energy orbital of any atom,characterized by n=1.I=m=0.It corre- sponds to the fundamental wave and is characterized by spherical symmetry and no electrons are placed in orbitals, the energy of the orbitals (and hence the energy of the electrons in them) is affected so that orbitals with the same principal quantum number n may vary in energy. Example. An electron in an orbital with a principal quantum number of n
2 can take on l values of 0 and 1, corresponding to 2s and 2p orbitals, respectively. Although these orbitals have the same principal quantum number and, therefore, the same energy when calculated for the single electron hydrogen atom, for the many-electron atoms, where electron–electron interactions become important, the 2p orbitals are higher in energy than the 2s orbitals. 1.27 MAGNETIC QUANTUM NUMBER ml This is the quantum number having values of the azimuthal quantum number from l to l that determines the orientation in space of the orbital angular momentum; it is represented by ml . Example. When n
2 and l
1 (the p orbitals), ml may thus have values of 1, 0, 1, corresponding to three 2p orbitals (see Sect. 1.35). When n
3 and l
2, ml has the values of 2, 1, 0, 1, 2 that describe the five 3d orbitals (see Sect. 1.36). 1.28 DEGENERATE ORBITALS Orbitals having equal energies, for example, the three 2p orbitals. 1.29 ELECTRON SPIN QUANTUM NUMBER ms This is a measure of the intrinsic angular momentum of the electron due to the fact that the electron itself is spinning; it is usually designated by ms and may only have the value of 1/2 or 1/2. 1.30 s ORBITALS Spherically symmetrical orbitals; that is, φ is a function of R(r) only. For s orbitals, l
0 and, therefore, electrons in such orbitals have an orbital magnetic quantum number ml equal to zero. 1.31 1s ORBITAL The lowest-energy orbital of any atom, characterized by n
1, l
ml
0. It corre￾sponds to the fundamental wave and is characterized by spherical symmetry and no 12 ATOMIC ORBITAL THEORY c01.qxd 5/17/2005 5:12 PM Page 12