Electronic Configuration PDF

Quantum Numbers, Atomic Orbitals, and Electron Configurations Each electron in an atom is described by four different quantum numbers. The first three (n, l, ml) specify the particular orbital of interest, and the fourth (ms) specifies how many electrons can occupy that orbital. 1. Principal Quant...

Quantum Numbers, Atomic Orbitals, and Electron Configurations Each electron in an atom is described by four different quantum numbers. The first three (n, l, ml) specify the particular orbital of interest, and the fourth (ms) specifies how many electrons can occupy that orbital. 1. Principal Quantum Number (n): n = 1, 2,…,8. This number describes the average distance of an electron from the nucleus, like the innermost electron shell, which has a principal quantum of 1.This specifies the energy of an electron and the size of the orbital. All orbitals that have the same value of n are said to be in the same shell (level). For a hydrogen atom with n=1, the electron is in its ground state; if the electron is in the n=2 orbital, it is in an excited state. The total number of orbitals for a given n value is n2. Orbitals for which n=2 are larger those for which n=1, for example. Because they have opposite electrical charges, electrons are attracted to the nucleus of the atom. Energy must therefore be absorbed to excite an electron from an orbital in which the electron is close to the nucleus (n=1) into an orbital in which it is further from the nucleus (n=2). The principal quantum number therefore indirectly describes the energy of an orbital. As n increases, the energies of the orbitals also increase. The principal quantum number n may have any positive integral value between n=1 and n= ∞. The n corresponds to the orbital energy level or ‘‘shell”. The shell with n=1 is called the 1st shell, the shell with n=2 is called the second shell and so forth. For a particular energy level, there may be subshell, the number of which is defined by the quantum number l. 2. Angular or orbital Quantum Number (l): l = 0,..., n-1. Specifies the shape of an orbital with a particular principal quantum number. The angular quantum number divides the shells into smaller groups of orbitals called subshells (sublevels). Usually, a letter code is used to identify l to avoid confusion with n: l 0 1 2 3 4 5... Letter s p d f g h... The subshell with n=2 and l=1 is the 2p subshell; if n=3 and l=0, it is the 3s subshell, and so on. The value of l also has a slight effect on the energy of the subshell; the energy of the subshell increases with l (s < p < d < f) 3. Magnetic Quantum Number (ml): ml = -l,..., 0,..., +l. Specifies the orientation in space of an orbital of a given energy (n) and shape (l). This number divides the subshell into individual orbitals which hold the electrons; there are 2l+1 orbitals in each subshell. Thus the s subshell has only one orbital, the p subshell has three orbitals, and so on 4. Spin Quantum Number (ms): ms = +½ or -½. Specifies the orientation of the spin axis of an electron. An electron can spin in only one of two directions (sometimes called up and down). The Pauli exclusion principle (Wolfgang Pauli, Nobel Prize 1945) states that no two electrons in the same atom can have identical values for all four of their quantum numbers. What this means is that no more than two electrons can occupy the same orbital, and that two electrons in the same orbital must have opposite spins. Because an electron spins, it creates a magnetic field, which can be oriented in one of two directions. For two electrons in the same orbital, the spins must be opposite to each other; the spins are said to be paired. These substances are not attracted to magnets and are said to be diamagnetic. Atoms with more electrons that spin in one direction than another contain unpaired electrons. These substances are weakly attracted to magnets and are said to be paramagnetic  Derive possible sets of quantum numbers for n=2 and explain the significance of these sets of numbers Let n=2 n-denotes an energy level l lies in the range 0 to (n-1) Therefore for n=2 l=0----(n-1) l=0-----(2-1) l=0----1 l=0 and 1. This means that the n=2 level gives rise to 2 sub-levels, one with l=0 and one with l=1 Now determine the possible values of quantum number ml Values of ml lie in the range -l ----0---+l When l=0 ml=-0----+0= 0 When l=1 ml=-1--0--+1=-1, 0, +1 Write down two possible sets of quantum numbers that describe an electron in a 2s atomic orbital. What is the physical significance of these unique sets? The 2s atomic orbital is defined by the set of quantum numbers n=2, l = 0, ml = 0. An electron in a 2s atomic orbital may have one of two sets of four quantum numbers: n=2, l = 0, ml = 0; ms = + 1/2 or n=2, l = 0, ml = 0; ms = - 1/2 If the orbital were fully occupied with two electrons, one electron would have ms = 1 + /2, and the other electron would have ms = - 1/ , i.e. the two electrons 2 would be spin paired. The Ground-state electronic configuration is the most probable or the most energetically favoured configuration. The Aufbau process Consider the following hypothetical process- the building up of more complex atom starting with the simplest atom, hydrogen. This hypothetical process is called Aufbau process (meaning building up in German) In this process we proceed from an atom of one element to the next by adding a proton and the requisite number of neutrons to the nucleus and one electron to the appropriate orbital. We pay particular attention to this added electron, called the differentiating electron. Hydrogen, Z =1. The lowest energy state for the electron in a hydrogen atom is the 1s orbital. The electronic configuration is 1s 1 Helium, Z =2. In the helium atom a second electron goes into the 1s orbital. The two electrons must have opposing spins, 1s2. Lithium Z=3. The differentiating electron cannot be accommodated in the 1s orbital (Pauli exclusion principle). It must be placed in the next lowest energy orbital 2s. The electron configuration is 1s22s1 Beryllium Z=4  SUMMARY Electrons in an atom are located in defined regions called electron shells, which surround the nucleus. This arrangement of electrons is referred to as the electron configuration.  There are ‘rules’ which determine how electron shells are filled, and how many electrons they can contain: Inner shells begin filling first; they are smaller and can hold less electrons.  A maximum of 2 electrons can occupy the first shell. A maximum of 8 electrons can occupy the second shell.  A maximum of 18 electrons can occupy the third shell, but the fourth shell will begin to fill once the third shell contains 8 electrons.  A maximum of 8 electrons can occupy the valence shell (outermost shell) of any atom, unless the valence shell is the only shell, in which case there can be a maximum of 2 electrons. The electron configuration of an atom can be written as the numbers of electrons in each shell, separated by a comma.