 # Unit 4 – Quantum Mechanics Cartoon courtesy of NearingZero.net.

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Unit 4 – Quantum Mechanics Cartoon courtesy of NearingZero.net

Light and Energy Much of what we know about electrons comes from study of light Light behaves as waves Light also behaves as particles (photons)

Wave properties Light waves are part of the electromagnetic spectrum
Can be characterized by 5 properties: Amplitude Wavelength Frequency Speed Energy

Electromagnetic radiation propagates through space as a wave moving at the speed of light.
C = speed of light, a constant (3.00 x 108 m/s)  = frequency, in units of hertz (hz, /s, s-1)  = wavelength, in meters

Calculating the color of light…
Given that a beam of light has frequency of 6.0 x 1014 /s what is the wavelength of this light? What color is it? –use p.129

E = h  = frequency, in units of hertz (hz, /s, s-1)
The energy (E ) of electromagnetic radiation is directly proportional to the frequency () of the radiation. This is the energy of a photon of a particular frequency. E = h E = Energy, in units of Joules (kg·m2/s2) h = Planck’s constant (6.63 x J·s)  = frequency, in units of hertz (hz, /s, s-1)

Long Wavelength = Low Frequency Low ENERGY Short Wavelength =
Wavelength Table Short Wavelength = High Frequency High ENERGY

Spectroscopic analysis of the visible spectrum…
(such as seen from an incandescent light bulb) …produces all of the colors in a “continuous spectrum”

Spectroscopic analysis of the hydrogen spectrum…
(as given off by a hydrogen gas-filled fluorescent light bulb) …produces a “bright line” or “emission spectrum”

Electron transitions occur when electrons absorb energy in a
‘quantum jump’ to an ‘excited state’. When they ‘fall’ back to their ’ ‘ground state’ they emit photons of light with distinct wavelengths, visible as bands on an ‘emission spectrum’ (not all are in the visible range). VISIBLE JUMPS

The Bohr Model of the Atom
I pictured electrons orbiting the nucleus much like planets orbiting the sun. But it turns out they’re more like bees around a hive. WRONG!!! Neils Bohr

Quantum Mechanical Model of the Atom
Mathematical laws were used to identify the regions outside of the nucleus where electrons are most likely to be found. These laws are beyond the scope of this class… But here are two important examples:

Schrodinger Wave Equation
Equation for probability of a single electron being found along a single axis (x-axis) Erwin Schrodinger

Heisenberg Uncertainty Principle
“One cannot simultaneously determine both the position and momentum of an electron.” You can find out where the electron is, but not where it is going. OR… You can find out where the electron is going, but not where it is! Werner Heisenberg

Electron Energy Level (Shell)
Generally symbolized by n, it denotes the average distance of the electron from the nucleus. Number of electrons that can fit in a shell: 2n2 1 holds holds holds 18 etc.

An orbital is a region within an energy level where there is a probability of finding an electron. This is a probability diagram for the… s orbital… in the first energy level. Orbital shapes are defined as the space that contains the electron 90% of the time.

1st: Energy Level (n = 1, 2, 3, 4 …) Average distance of the electron in the electron cloud from the nucleus. 2nd: Sublevel (l = s, p, d, f) Shape of electron cloud. energy levels have n sublevels. 3rd: Orbital (ml) Orientation of the cloud in 3-D space. s sublevels have 1 orbital (spherical) p sublevels have 3 orbitals (dumb bell shape) d sublevels have 5 orbitals (varied) f sublevels have 7 orbitals (varied) 4th: Spin (ms = +1/2 or -1/2) Direction of electron spin. Each orbital holds 2 electrons, one with each spin.

Pauli Exclusion Principle: Each electron of an atom has its own unique set of quantum numbers. They may have three that are the same, but never all four.

Sizes of s orbitals Orbitals of the same shape (s, for instance) grow
larger as n increases… Nodes are regions of low probability within an orbital.

The s orbital the origin of the three axes in space
has a spherical shape centered around the origin of the three axes in space There is only one orientation for this shape

P orbital shape There are three dumbbell-shaped p orbitals in
each energy level above n = 1, each assigned to its own axis (x, y and z) in space.

To remember the shapes, think of “double dumbells”
Things get a bit more complicated with the five d orbitals that are found in the d sublevels beginning with n = 3. To remember the shapes, think of “double dumbells” d orbital shapes …and a “dumbell with a donut”!

In case you are too curious, here is what the f orbitals look like.

Energy Levels, Sublevels, Electrons
Sublevels in main energy level (n sublevels) Number of orbitals per sublevel Electrons per sublevel electrons per level (2n2) 1 2 3 4 s s p s p d d f

The Diagonal Rule: Sublevels in order of increasing energy
1s22s22p63s23p64s23d104p65s24d105p66s24f145d106p67s25f14… The Diagonal Rule: Sublevels in order of increasing energy 5g18 6f14 7d10 8p6 8s2 4f14 5f14 3d10 4d10 5d10 6d10 2p6 3p6 4p6 5p6 6p6 7p6 1s2 2s2 3s2 4s2 5s2 6s2 7s2 Aufbau Principle: Electrons fill the lowest energy position available.

Energy levels and sublevels on the Periodic Table

Hund’s Rule: Electrons fill orbitals so that there are a maximum number of orbitals with a single electron.

Element notation Orbital notation
Configuration notation Orbital notation Noble gas Lithium 1s22s1 ____ ____ ____ ____ ____ 1s s p [He]2s1 Beryllium 1s22s2 [He]2s2 Boron 1s22s22p1 [He]2s2p1 Carbon 1s22s22p2 [He]2s2p2 Nitrogen 1s22s22p3 1s s p [He]2s2p3 Oxygen 1s22s22p4 [He]2s2p4 Fluorine 1s22s22p5 [He]2s2p5 Neon 1s22s22p6 [He]2s2p6

Electron configuration of the elements of the first three periods