# Atomic Theory and Spectroscopy

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Atomic Theory and Spectroscopy

Energy emitted by electrons can be detected at any part of the electromagnetic spectrum

So, just what is EMR? - an oscillating electric and magnetic field which travels through space OR - a discrete series of “particles” that possess a specific energy but have no mass BOTH!

Waves

Measuring Waves Two properties can be measured: Wavelength (l)
The distance from the same point on successive waves (measured in meters)

Measuring Waves Frequency ()
The number of times a wave travels up and down per second Measured in cycles per second or hertz (Hz)

The frequency () is the number of wave crests per second which pass a reference point.

The amplitude (A) is the height of the wave

Measuring Radiation All radiation constantly travels through space at the same velocity (speed) = 3.0 x 108 m/s (299,792,458 meters per second) The speed of electromagnetic radiation ---“The speed of light” = c

c=  l c = 3.0 x108 If either the frequency or wavelength is known, the other can be calculated

A red light has a wavelength of 728 *10-9 m.
What is the speed of the wave in m/s?    What is the frequency of the light?

A certain blue light has a frequency of 6. 91 x 1014 Hz
A certain blue light has a frequency of 6.91 x 1014 Hz. What is the wavelength of the light?

Determine the wave length of light with a speed of 50*106 Hz (/sec)

If I have a wavelength of 780 *10-9 m and what is the frequency?

Microwave ovens often employ radiation with a frequency of 2
Microwave ovens often employ radiation with a frequency of 2.45 x 109 /s. What is the wavelength (in cm) of this radiation?

A purple light has a frequency of 7. 42 x 1014 Hz
A purple light has a frequency of 7.42 x 1014 Hz.      What is its wavelength?     What is the energy of one quanta of light

m/s Not just a good idea, it’s the law!

Properties of Light Form of energy, detectable with the eye, which can be transmitted from one place to another at a finite velocity

Theory of Light •Two complimentary theories to explain
how light behaves and the form by which it travels: Particle Theory Wave Theory

Particle Theory • Release of a photon

Electromagnetic spectrum and Energy
longest

Planck’s Quantum Theory
In 1900, German Physicist Max Planck proposed: “Radiant energy may only be absorbed or emitted in discrete amounts: quanta.”

Electromagnetic spectrum and Energy
Planck discovered the energy of a wave or photon of light is constant h = (6.63 x 10-34J/Hz) Planck’s constant (h)

Energy and Radiation If the frequency of a wave is known, then the energy of the wave can be calculated as well in the same manner E=h  Or E= h (c/)

Energy and Radiation  = 1.035 x 108 Hz E=hv
Sample: What is the energy of a wave which has a frequency of x 108 Hz? 6.63 x10-34 J 1.035 x 108 Hz E = 6.86 x 10-26J = Hz  = x 108 Hz 6.63 x10-34 J h = Hz

Photons Photons are a particle of radiation or an individual quantum of light Quantum is a finite quantity of energy that can be gained or lost by an atom

The Nature of Light and Radiation
If e- are exposed to energy which matches those levels (a photon), they leap to unstable higher energy levels. As they fall back they emit that energy ( a photon) at a wavelength and frequency which can be detected.

Photoelectric Effect Albert Einstein proposed that light not only behaves as a wave, but as a particle too Albert Einstein did not get the Nobel Prize for Relativity. He received it for work that he did between 1905 and 1911 on the Photoelectric Effect.

Photoelectric Effect In 1905, Einstein applied this quantum theory to
explain the photoelectric effect:

Photoelectric Effect -if EMR was absorbed as a wave, then the number of electrons ejected and the energy of the electrons ejected should vary only with the intensity of the light

Einstein Photoelectric Effect
hv Ehv - Ee- = Ionization Energy

Photoelectric Effect NUMBER of e-: does vary with EMR intensity
ENERGY of e-: vary only with MR frequency AND: no effect if freq is below a threshold value!

Photoelectric effect The reason that certain types of light cause this effect but others do not has to do with threshold energy Remember that electrons must gain energy in certain amounts (E = h) Only certain types of light with “just the right” frequency can cause electrons to become excited

The Nature of Light and Radiation

Photoelectric Effect View EMR as a collection of particles(called
photons), with each photon having the following energy: E = hν

Photoelectric Effect Each photon will cause an electron to be ejected
IF the energy of the photon is above a minimum (threshold) value. Any energy of the photon above that needed to eject the electron would be transferred to the electron as kinetic energy

Photoelectric Effect Increased EMR intensity translates to an increase in the number of photons (increasing the number of electrons ejected)

Einstein Einstein did not receive his Nobel Prize of the theory of relativity but for his work on the photoelectric effect

Typed of Spectra

Hydrogen Line Spectrum
Because hydrogen atoms emit only specific frequencies of light indicate that the energy differenced between the atom states are fixed

The Bohr Atom The electron in a hydrogen atom can exist only in discrete orbits The orbits are circular paths about the nucleus at varying radii

Electrons exist in specific, discrete levels or quanta of energy The lowest energy of each electron is known as its ground state If the right amount (quantum) of energy is applied, then an electron will “leap” to another energy level

The Bohr Atom Each orbit corresponds to a particular energy
Orbit energies increase with increasing radii

The Bohr Atom The lowest energy orbit is called the ground state
After absorbing energy, the e- jumps to a higher energy orbit (an excited state)

The Bohr Atom When the e- drops down to a lower energy orbit, the energy lost can be given off as a quantum of light The energy of the photon emitted is equal to the difference in energies of the two orbits involved

Bohr’s Model of H Atom Linked an atom’s e- to photon emission
Said that e’ can circle the nucleus only is specific paths or orbits. Orbits are separated from the nucleus by large empty spaces (nodes) where the e- cannot exist. (Rungs on a ladder) Remember, E increases as e- are further from the nucleus.

Bohr’s Model of H Atom While an e- is in orbit, it cannot gain nor lose E It can, move to a higher E level IF it gains the amount of E = to the difference between the higher E orbit and the lower energy orbit. When falls, it emits a PHOTON = to the difference. Absorption gains E/Emission gives off E

Take the good with the bad (Bohr’s Model)
Led scientists to believe a similar model could be applied to all atoms. Bad: Yikes!!! Did not explain the spectra of atoms with more than one e’ or chemical behavior of atoms!

The Bohr Model of the Atom
I pictured electrons orbiting the nucleus much like planets orbiting the sun. But I was wrong! They’re more like bees around a hive. WRONG!!! Neils Bohr

The Nature of Electrons
If light acts as both particles and waves, then so do electrons. If electrons act like waves, then how can we locate them?

Atoms are like onions and ogres they have lots of layers

Orbits We like to draw orbits as circular but they really aren’t

Orbits Turns out, there's no reason to assume that electron orbits are circular.

Orbits There are lots of paths an electron can take in order to get around the nucleus. (or through the nucleus)

Orbits In fact it's very rare for an atom's electron to be in a circular orbit.

Electron Facts The electron moves at different speeds. Fast near the nucleus and slow when it's far from the nucleus.

Well we really don’t Because atoms are so small, no one can see them.
For this reason, we just can't say exactly where the electron is, as it moves about the nucleus. In those orbit pictures, we know the electron will be somewhere on the white orbit lines.

This makes the models involving orbits, whether circles, or ellipses, wrong, because the orbits are pretty specific about the electron's location.

So how do we locate electrons in the modern atom?
Quantum Numbers

Quantum Numbers Specify the properties of atomic orbitals and the properties of electrons in orbital

Quantum Numbers Don’t tell us where the electron is, just where it's most likely to be. The probable location of electrons are described using an address

The four quantum numbers
their symbols are n, l, m and s. EVERY electron in an atom has a specific, unique set of these four quantum numbers.

Quantum Numbers There are 4 parts to each address
Principle quantum number (n) Angular quantum number (l) Magnetic quantum number (m) Spin quantum number (s)

The Principal Quantum Number
The main energy level of an electron

Principal Quantum Number (n)
Describes the size of the orbital. Since the distance from of an electron from the nucleus is directly proportional to the energy of the electron It must be a whole number n=1, n=2 …

Angular quantum number (l) Azimunthal
Describes the shape The secondary quantum number divides the shells into smaller groups of orbitals called subshells (sublevels). s p d f g h...

Angular (Azimuthal) Momentum Quantum Number
Letter Shape s Sphere p Dumbell d Cloverleaf f “funky”

Each suborbital can hold a maximum of 2 electrons per orbital

Angular (Azimuthal) Momentum Quantum Number
Letter Max number of suborbitals Max. # of e- s 1 2 p 3 6 d 5 10 f 7 14

Quantum Numbers The more crowded the dots are in a particular region, the better chance you have to finding your electron there.

s Orbital sphere

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.

p Orbital dumbbell

two p Orbitals

All three p Orbitals

orbital                         d Orbitals Cloverleaf

orbital                         f Orbitals “funky”

Orbital filling table

The Magnetic Quantum Number
describes the orientation in space of a particular orbital. x, y, z It is called the magnetic quantum number because the effect of different orientations of orbitals was first observed in the presence of a magnetic field.)

Magnetic quantum number (m)
The orientation in space What axis the orbit is located on

The Spin Quantum Number
allows two electrons of opposite spin (or symmetry) into each orbital. +1/2 or -1/2  or 

Spin quantum number (s)
+1/2 -1/2

Aufbau (filling up) Principle
the number of electrons in an atom is equal to the atomic number each added electron will enter the orbitals in the order of increasing energy an orbital can only hold 2 electrons.

Hund’s Rule For orbitals of equal energy, one electron goes into each orbital until all orbitals are half-full. 2p4 2s2 1s2

Aufbau Principle Lower-energy orbitals of an atom are filled with electrons first. 1s 2s 2p 3s 3p 4s 3d 4p …

Pauli Exclusion Principle
No two electrons in an atom can have an identical set of four quantum numbers. (electrons sharing an orbital have different spins) 2s2 1s2

Key Terms Ground State Electron Configurations (1s22s2…/Orbital Notations __ __ __ __ Aufbau Principle (lowest first/periodic guide) Hund’s Rule: Single e’ before pairing begins Pauli Exclusion (up/down—no 2 e’ same set of quant. #’s) Highest Occupied Level Inner-Shell e’ Noble Gas Notation

Spin Diagram for Hydrogen
Electron configuration for Hydrogen 1s1

Spin Diagram for Helium
Electron configuration for Helium 1s2

Spin Diagram for lithium
Electron configuration for lithium 1s22s1

Spin Diagram for beryllium
Electron configuration for berylium 1s22s2

Electron configuration
Spin Diagram for boron Electron configuration for boron 1s22s22p1

Spin Diagram for carbon
Electron configuration for carbon 1s22s22p2

Spin Diagram for nitrogen
Electron configuration for nitrogen 1s22s22p3

Spin Diagram for oxygen
Electron configuration for oxygen 1s22s22p4

Spin Diagram for fluorine
Electron configuration for fluorine 1s22s22p5

Electron configuration
Spin Diagram for neon Electron configuration for neon 1s22s22p6

Standard Notation or Complete electron configuration of Fluorine
Number of electrons in the sub level 2,2,5 1s2 2s2 2p5 Main Energy Level Numbers 1, 2, 2 Sublevels

Shorthand Notation or Noble Gas Configuraiton
Use the last noble gas that is located in the periodic table right before the element. Write the symbol of the noble gas in brackets. Write the remaining configuration after the brackets. Ex: Fluorine: [He] 2s2 2p5

Blocks in the Periodic Table

You broke your big toe!  The x ray they take of  toe uses waves that have a length 2.19 x 1010m.      What is the speed of the wave in m/s?      What is the wavelength in nm?      What is the frequency of the x ray?