MULTIELECTRON ATOMS l ELECTRON SPIN: Electron has intrinsic angular momentum - “spin”; it behaves as if it were “spinning”, i.e. rotating around its axis. rotating charge  magnetic field - the electron is a magnetic dipole. S = sħ with s =  remember: ħ = h/2  is the “unit of angular momentum” (In units of angular momentum,) the electron has “spin”; it is a member of the family of particles with “half-integer spin”, called “Fermions”. Fermions obey Pauli's exclusion principle. direction of spin is “quantized”, i.e. only certain directions are allowed. For spin 1/2, only two directions are allowed - called “up” and “down”. l PAULI'S EXCLUSION PRINCIPLE No quantum mechanical state can be occupied by more than one fermion of the same kind (e.g. more than one electron). l MULTIELECTRON ATOMS The hydrogen atom, having only one electron, is a very simple system; this is why Bohr's simple model worked for it. Complications in atoms with many electrons:  in addition to the force between electron and nucleus, there are also forces between the electrons;  “shielding”: electrons in outer orbits are shielded from the force of the nucleus by electrons in the inner orbits.   need to solve Schrödinger equation to describe multi- electron atoms.

QUANTUM NUMBERS l Schrödinger equation applied to atom  : electron's energy, magnitude and direction of angular momentum are quantized (i.e. only certain values allowed); no well-defined orbit, only probability of finding electron at given position “orbital”; the state of an electron is described by a set of four quantum numbers:  n, the principal quantum number  l, the orbital quantum number  m l = l z, the orbital magnetic quantum number  m s = s z, the spin quantum number Meaning of quantum numbers:  the energy level of a state is determined by n and l  most probable value of distance grows with n  n = 1,2,3,….  l = 0,1,2,3,…, n -1 (i.e. n different values); measures magnitude of angular momentum in units of ħ ; value of l influences the energy and the shape of the orbital:  l = 0 : spherical  l = 1 : dumbbell shaped,....  m l = 0,  1,  2,  l, i.e. (2 l + 1) different values; specifies direction of angular momentum (gives component of angular momentum vector in specified direction)  determines orientation of orbital  m s =   denotes direction of spin : m s = +  “spin up” m s =   “spin down”

orbitals l Orbital shapes

Electron “shells” l Some definitions: collection of orbitals with same n: “electron shell”; shells named K,L,M,N,.. one or more orbitals with same n and l : “subshell”; spectroscopic notation for orbitals: orbitals denoted by value of n and a letter code for the value of l :  l = 0: s  l = 1: p  l = 2: d  l = 3: f  l = 4: g  and alphabetic after that;  e.g.: “2s” refers to the subshell n=2, =0;  number of electrons in the subshell is added as a superscript;  e.g.: “2p 6 means a configuration where 6 electrons are in the subshell 2p, i.e the subshell with n = 2 and l = 1. l PAULI EXCLUSION PRINCIPLE  : No two electrons in the same atom can have the same set of four quantum numbers  the number of electrons in a given subshell is limited to 2x(2 l + 1) (factor of 2 is due to orientation of spin), number of electrons in a given shell is limited to 2n 2.  in multi-electron atom, electrons cannot all sit in the lowest energy levels.

Electron configurations of the elements Periods 1,2, 3,4 period 5

Electron configuration, cont’d l Period 6

Electron configuration, cont’d Period 7