QUANTUM MECHANICAL MODEL OF THE ATOM

DEFINITION OF TERMS QUANTUM – UNIT OF ENERGY ORBITALS – space around a nucleus where the probability of finding an electron is greatest. QUANTUM NUMBERS – set of four numbers used to describe the electron’s energy level in terms of: a. distance from the nucleus b. shape of the orbital c. orientation in space (x, y, z) d. direction of electron spin (clockwise, counter-clockwise)

ENERGY LEVELS OF THE ATOMIC ORBITALS 1. MAIN ENERGY LEVEL (MEL). - represents the average distance of the electrons from the nucleus. - values 1, 2, 3, 4, 5, 6 and 7

Electrons in MEL closer to the nucleus have the lowest energy

2. SUBLEVELS or SUBSHELLS - define the shapes of the orbitals - has four possible shapes called s, p, d and f EACH SUBLEVEL HAS DIFFERENT NUMBERS OF ORBITALS AND EACH ORBITAL CAN ONLY HAVE A MAXIMUM OF 2 ELECTRONS

s p d f 1 orbital – 2 electrons 3 orbitals – 6 electrons

SUMMARY OF ENERGY LEVELS, ORBITALS AND ELECTRON RELATIONSHIPS MEL (n) MAXIMUM NUMBER OF ORBITALS (n2) MAXIMUM NUMBER OF ELECTRONS PER ENERGY LEVEL (2n2) 1 2 4 8 3 9 18 16 32

ELECTRONIC CONFIGURATION - Process of arranging the electrons around the nucleus The problem? The solution!

THE RESULT!!!

RULES GOVERNING ELECTRON CONFIGURATION AUFBAU PRINCIPLE – electrons enter orbitals of lowest energy first. PAULI’S EXCLUSION PRINCIPLE – only two electrons can occupy a single orbital. HUND’S RULE OF MAXIMUM MULTIPLICITY– within the same sublevel, electrons prefer to occupy empty rather than half-filled orbitals.

What is the electron configuration of Oxygen? 2s 2p 3s 3p 3d 4s 4p 4d 4f 5s 5p 5d 5f 6s 6p 6d 7s 7p Oxygen has 8 electrons. Its electron configuration is: 1s 2 2s 2 2p 4 2 + 2 + 4 = 8 electrons

ELECTRON CONFIGURATION OF IONS What is the electron configuration of S 2- ? SOLUTION: 1. Solve for the total number of electrons. e - = p+ - c = 16 – (-2) = 18 2. Use the electron configuration chart 1s2 2s2 2p6 3s2 3p6 3. Check the number of electrons used. 2 + 2 + 6 + 2 + 6 = 18

√ √ EXCEPTIONS TO THE RULE 24Cr 1s2 2s2 2p6 3s2 3p6 4s2 3d4 29Cu 1s2 2s2 2p6 3s2 3p6 4s2 3d9 1s2 2s2 2p6 3s2 3p6 4s1 3d10 √ √

Electron Population Distribution - Shows how the electrons are distributed among the different orbitals - Based on the electron configuration of the elements

Electron Population Distribution Show the electron population distribution for 15P. P has 15 electrons. Its electron configuration is 1s2 2s2 2p6 3s2 3p3. The electron population distribution for P is: 1s 2s 2p 3s 3p

Set of 4 numbers used to describe the electrons in terms of : QUANTUM NUMBERS Set of 4 numbers used to describe the electrons in terms of : Distance from the nucleus Shape of the orbitals Orientation in space Direction of electron spin

PRINCIPAL QUANTUM NUMBER, n Refers to the main energy levels Related to the average distance of the electron from the nucleus Can only have integral values of n = 1, 2, 3, 4 etc.

AZIMUTHAL or SECONDARY QUANTUM NUMBER, l Defines the shape of the orbital. Also refers to the energy sublevels subshell Azimuthal quantum number, l s p 1 d 2 f 3

MAGNETIC QUANTUM NUMBER, ml Describes the orientation of the orbitals in space. The range of magnetic quantum numbers defined by the formula ml = 2l + 1 and takes the integer value between –l to +l including 0 subshell Possible magnetic quantum numbers, m l s p -1, 0, +1 d -2, -1, 0, +1, +2 f -3, -2, -1, 0, +1, +2, +3

SPIN QUANTUM NUMBER, ms - differentiates how two electrons behave under a magnetic field. Can only have two possible values +½ and -½

Example. What are the possible quantum numbers for the outermost electron of oxygen? SOLUTION: Identify the final orbital occupied by the electron. 1s2 2s2 2p4 n = l = ml = ms = 2 2 p4 1 -1, 0, +1 +½ , -½

What are the possible quantum numbers for the outermost electron of chromium? SOLUTION: Identify the final orbital occupied by the electron. 1s2 2s2 2p6 3s2 3p6 4s1 3d5 n = l = ml = ms = 3 3 d5 2 -2, -1, 0, +1, +2 +½ , -½

For each subshells given below, give the maximum number of orbitals and electrons possible Subshell or sublevel Number of orbitals Number of electrons 8s 3p 3d 6f 6s 5d 4f

Electron Population Distribution or Electron Orbital Notation Show the electron population distribution for 15P. P has 15 electrons. Its electron configuration is 1s2 2s2 2p6 3s2 3p3. The electron population distribution for P is: 1s 2s 2p 3s 3p