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Quantum Numbers Basics of Periodic Table • Each box on the table represents an element. • In each box… – an element symbol – the element’s atomic number – the element’s average atomic mass • Elements arranged in order of increasing atomic number. Remember… • Aufbau principle – electrons fill energy levels and sublevels in order of increasing energy • Pauli Exclusion principle – no two electrons can have the same set of four quantum numbers (which means no two electrons can be in the same place at the same time) • Hund’s rule – when adding electrons to sublevels with more than one orbital, each orbital gets its own electron first before pairing Also…. • There are energy levels (AKA shells) • Inside energy levels, there are sublevels (AKA subshells) • Inside sublevels, there are orbitals • Inside orbitals, there are electrons. The Basics of the 4 QN • Principle Quantum number (or 1st QN) tells you the energy level • 2nd Quantum number tells you which sublevel (s, p, d, or f) • 3rd Quantum number tells you which orbital of that sublevel • 4th Quantum number tells you the spin direction of the electron Principal Quantum number • Tells you the relative electron cloud size – The higher the quantum number, the larger the cloud • Corresponds to the rows on the periodic table – 1st energy level = Row 1 – 2nd energy level = Row 2, etc • You can determine how many electrons are possible within any energy level by using the formula 2n2 (where n is the energy level #) 2nd Quantum number • Tells you the shape of the electron cloud – The “s” sublevel is spherical – The “p” sublevel is dumbbell shaped – The “d” and “f” sublevels are unusually shaped • Can also determine how many sublevels are within an energy level – Energy Level 1 has 1 sublevel (s) – Energy level 2 has 2 sublevels (s and p) – Energy level 3 has 3 sublevels (s, p, and d) – Energy level 4 has 4 sublevels (s, p, d, and f)) s orbitals p orbitals d orbitals f orbitals 3rd Quantum Number • Tells you the orientation in space of the sublevel – Does it surround the origin? (s orbital) – Do they lie on the x-, y-, or z- axis? (p orbitals) • Defines how many orbitals are contained in a sublevel. – s sublevel has 1 orbital – p sublevel has 3 orbitals – d sublevel has 5 orbitals – f sublevel has 7 orbitals 4th Quantum number • Tells you that there can be only 2 electrons per orbital and they must have opposite spins – This is known as the Pauli Exclusion Principle • Which means that no two electrons can be in the same place at the same time • The electrons will be either going clockwise or counterclockwise. Drawing Energy Levels Ground State vs Excited State • In a ground state atom, all electrons are in the lowest available sublevels. • For an atom in the excited state, one or more electrons have absorbed enough energy to jump to higher energy levels. – As soon as possible, those excited electrons will release that energy in the form of a photon, possibly as colored light. Energy • The above is called an aufbau diagram. • When using an aufbau diagram, it is easy to place electrons following the aufbau principle. • But, when using strips of boxes (like a previous slide), you need to follow the diagonal rule. Better yet…. Learn to read the periodic table. Blank Periodic table revisited How the sublevels relate to the periodic table • The s sublevel has only one orbital, which can hold 2 electrons. That is why there are two columns in the “s” block. • The p sublevel has three orbitals, each of which can hold 2 electrons. That is why there are six columns in the “p” block. • The d sublevel has five orbitals, each of which can hold 2 electrons. That is why there are ten columns in the “d” block. • The f sublevel has seven orbitals, each of which can hold 2 electrons. That is why there are fourteen columns in the “f” block. Schrödinger’s Equation • This is not a “derivable” equation. • This is called an “inspired” equation • Somehow, from this equation the four quantum numbers were born. Quantum Numbers • Just as a point on an xy-graph needs a set of two coordinates, each electron has a unique set of four coordinates. • These four coordinates represent energy level (shell), sublevel (subshell), orbital, and spin direction of the electron. Principal Quantum number • • • • Represented by n Tells the size of the electron cloud Corresponds to the rows of the periodic table Therefore n = 1, 2, 3, and so on – Which means row 1 on the periodic table corresponds to energy level 1 2nd Quantum number • Represented by l • Called the angular momentum quantum number • Describes the shape of the orbital • l can have the values from 0 to n-1 (where n is the row number) 0 = s sublevel 1 = p sublevel 2 = d sublevel 3 = f sublevel 3rd Quantum Number • Called the magnetic quantum number • Describes the orientation in space of the orbital – Whether the path of the electron lies on the x, y, or z axis • Represented by ml • ml can have values from –l to +l – if l = 2, then ml = -2, -1, 0, +1, +2 4th Quantum Number • • • • Corresponds to the spin of an electron Represented by ms Clockwise represented by +1/2 Counterclockwise represented by -1/2 Therefore • Mg (3, 0, 0, -1/2) • Bi (6, 1, +1, +1/2) • Co (3, 2, -1, -1/2) • Cf (5, 3, -1, -1/2) Diamagnetism/Paramagnetism • Diamagnetic elements have all of their electrons spin paired. – Which means they have complete sublevels. – Are not affected by a magnetic field • Paramagnetic elements do not have all of their electrons spin paired. – Strongly affected by a magnetic field