QUANTUM MECHANICS -C. FAULK CHEMISTRY II

Electron clouds Although we cannot know how the electron travels around the nucleus we can know where it spends the majority of its time (thus, we can know position but not trajectory). The “probability” of finding an electron around a nucleus can be calculated. Relative probability is indicated by a series of dots, indicating the “electron cloud”. 90% electron probability/cloud for 1s orbital (notice higher probability toward the centre)

4 QUANTUM NUMBERS The shape, size, and energy of each orbital is a function of 4 quantum numbers which describe the location of an electron within an atom or ion n (principal) ---> energy level l (orbital) ---> shape of orbital m l (magnetic) ---> designates a particular suborbital The fourth quantum number is not derived from the wave function s(spin) ---> spin of the electron (clockwise or counterclockwise: ½ or – ½) s (spin) ---> spin of the electron (clockwise or counterclockwise: ½ or – ½)

Schrodinger Wave Equation In 1926 Schrodinger wrote an equation that described both the particle and wave nature of the e - Wave function (  ) describes: 1. energy of e - with a given  2. probability of finding e - in a volume of space Schrodinger’s equation can only be solved exactly for the hydrogen atom. Must approximate its solution for multi-electron systems. 7.5

Schrodinger Wave Equation  = fn(n, l, m l, m s ) Shell – electrons with the same value of n Subshell – electrons with the same values of n and l Orbital – electrons with the same values of n, l, and m l How many electrons can an orbital hold? If n, l, and m l are fixed, then m s = ½ or - ½  = (n, l, m l, ½ ) or  = (n, l, m l, - ½ ) An orbital can hold 2 electrons 7.6

Schrodinger Wave Equation  fn(n, l, m l, m s ) principal quantum number n n = 1, 2, 3, 4, …. n=1 n=2 n=3 7.6 distance of e - from the nucleus

 = fn(n, l, m l, m s ) spin quantum number m s m s = +½ or -½ Schrodinger Wave Equation m s = -½m s = +½ 7.6

Existence (and energy) of electron in atom is described by its unique wave function . Pauli exclusion principle - no two electrons in an atom can have the same four quantum numbers. Schrodinger Wave Equation  = fn(n, l, m l, m s ) Each seat is uniquely identified (E, R12, S8) Each seat can hold only one individual at a time 7.6

Properties of Waves Frequency ( ) is the number of waves that pass through a particular point in 1 second (Hz = 1 cycle/s). The speed (u) of the wave = x 7.1

Properties of Waves Wavelength ( ) is the distance between identical points on successive waves. Amplitude is the vertical distance from the midline of a wave to the peak or trough. 7.1

Maxwell (1873), proposed that visible light consists of electromagnetic waves. Electromagnetic radiation is the emission and transmission of energy in the form of electromagnetic waves. Speed of light (c) in vacuum = 3.00 x 10 8 m/s All electromagnetic radiation x  c 7.1

7.3

Electron configuration is how the electrons are distributed among the various atomic orbitals in an atom. 1s 1 principal quantum number n angular momentum quantum number l number of electrons in the orbital or subshell Orbital diagram H 1s 1 7.8

Periodic table arrangement the quantum theory helps to explain the structure of the periodic table. n - 1 indicates that the d subshell in period 4 actually starts at 3 (4 - 1 = 3).

Outermost subshell being filled with electrons 7.8

Order of orbitals (filling) in multi-electron atom 1s < 2s < 2p < 3s < 3p < 4s < 3d < 4p < 5s < 4d < 5p < 6s 7.7

What is the electron configuration of Mg? Mg 12 electrons 1s < 2s < 2p < 3s < 3p < 4s 1s 2 2s 2 2p 6 3s = 12 electrons 7.8 Abbreviated as [Ne]3s 2 [Ne] 1s 2 2s 2 2p 6 What are the possible quantum numbers for the last (outermost) electron in Cl? Cl 17 electrons1s < 2s < 2p < 3s < 3p < 4s 1s 2 2s 2 2p 6 3s 2 3p = 17 electrons Last electron added to 3p orbital n = 3l = 1m l = -1, 0, or +1m s = ½ or -½

Shorthand Notation Step 1: Find the closest noble gas to the atom (or ion), WITHOUT GOING OVER the number of electrons in the atom (or ion). Write the noble gas in brackets [ ]. Step 2: Find where to resume by finding the next energy level. Step 3: Resume the configuration until it’s finished.

Try These! Write the shorthand notation for: Cu W Au [Ar] 4s 1 3d 10 [Xe] 6s 1 4f 14 5d 5 [Xe] 6s 1 4f 14 5d 10

Why are d and f orbitals always in lower energy levels? d and f orbitals require LARGE amounts of energy and have too many electrons to be valence (more than 8) It’s better (lower in energy) to skip a sublevel that requires a large amount of energy (d and f orbtials) for one in a higher level but lower energy This is the reason for the diagonal rule! BE SURE TO FOLLOW THE ARROWS IN ORDER!

Exceptions to the Aufbau Principle Remember d and f orbitals require LARGE amounts of energy If we can’t fill these sublevels, then the next best thing is to be HALF full (one electron in each orbital in the sublevel) There are many exceptions, but the most common ones are d 4 and d 9 For the purposes of this class, we are going to assume that ALL atoms (or ions) that end in d 4 or d 9 are exceptions to the rule. This may or may not be true, it just depends on the atom.

Exceptions to the Aufbau Principle d 4 is one electron short of being HALF full In order to become more stable (require less energy), one of the closest s electrons will actually go into the d, making it d 5 instead of d 4. For example: Cr would be [Ar] 4s 2 3d 4, but since this ends exactly with a d 4 it is an exception to the rule. Thus, Cr should be [Ar] 4s 1 3d 5. Procedure: Find the closest s orbital. Steal one electron from it, and add it to the d.

Keep an Eye On Those Ions! Electrons are lost or gained like they always are with ions… negative ions have gained electrons, positive ions have lost electrons The electrons that are lost or gained should be added/removed from the outermost energy level (not the highest orbital in energy!)

Keep an Eye On Those Ions! Tin Atom: [Kr] 5s 2 4d 10 5p 2 Sn +4 ion: [Kr] 4d 10 Sn +2 ion: [Kr] 5s 2 4d 10 Note that the electrons came out of the highest energy level, not the highest energy orbital!

Shapes and Orientations of Orbitals

s orbitals d orbitals Number of orbitals Number of electrons p orbitals f orbitals 7 14 How many electrons can be in a sublevel? Remember: A maximum of two electrons can be placed in an orbital.

Types of Orbitals ( l ) s orbital p orbital d orbital

p Orbitals this is a p sublevel with 3 orbitals These are called x, y, and z this is a p sublevel with 3 orbitals These are called x, y, and z There is a PLANAR NODE thru the nucleus, which is an area of zero probability of finding an electron 3p y orbital

f Orbitals For l = 3, f sublevel with 7 orbitals

Summary: p orbitals and d orbitals p orbitals look like a dumbell with 3 orientations: p x, p y, p z (“p sub z”). Four of the d orbitals resemble two dumbells in a clover shape. The last d orbital resembles a p orbital with a donut wrapped around the middle.

Heisenberg’s uncertainty principle Electrons are difficult to visualize. As a simplification we will picture them as tiny wave/particles around a nucleus. The location of electrons is described by: n, l, m l n = size, l = shape, m l = orientation Heisenberg showed it is impossible to know both the position and velocity of an electron. Think of measuring speed & position for a car. Fast Slo w

Heisenberg’s uncertainty principle The distance between 2+ returning signals gives information on position and velocity. A car is massive. The energy from the radar waves will not affect its path. However, because electrons are so small, anything that hits them will alter their course. The first wave will knock the electron out of its normal path. Thus, we cannot know both position and velocity because we cannot get 2 accurate signals to return.

4s 3s 2s 1s 2p 3p 3d ENERGYENERGYENERGYENERGY n l mlml msms 10(s) 2 1(p) ,10, 30(s) 1(p) 0 -1,10, 2(d) -1,1,0, -2, 2 40(s)0 Movie: periodic table of the elements: t10-20