ATOMIC STRUCTURE

 Characterize wave forms of energy in terms of frequency, speed, wavelength, and amplitude. Understand the mathematical relationship between frequency, wavelength, and speed of an electromagnetic wave.  Understand and describe the Bohr model of the atom including restricted energy levels for electrons and what happens when electrons transition from one energy level to another.  Gain a basic understanding of the quantum model of the atom and the significance of the term orbital in describing the behavior of an electron.  Be familiar with the major contributors to the quantum model of the atom including Bohr, Heisenberg, Einstein, Planck, deBroglie, and Schroedinger.  Describe the allowed energy states of electrons using the system of quantum numbers.

 #1 – 21, 23, 25, 27, 29, 67, 69 Electromagnetic Radiation, Spectrum, Energies  #2 –47, 49, 51, 53, 55, 57, 59, 61, 63, 73, 87,  Quantum Mechanics and Quantum #’s

 Introduction  Flaw in Rutherford’s Model RECALL: Rutherford and Bohr’s Contributions and Models of the Atom! FLAW: Electrons are particles that travel in orbits  Problem for 20th century scientists Model didn’t work for larger atoms, only for small ones like H 2

 The nature of light – a side trip Light is not matter…………or is it?!?  Wave-Particle Duality? Light has properties that are both wave-like and particle- like Particle-like: packets of energy called photons

 2.Electromagnetic Radiation – definition  Energy in the form of a wave resulting from oscillating electric and magnetic fields  ALL forms of light, both visible and invisible to the human eye  Lowest to highest energy

 4. Properties of waves  Wavelength ( ): distance between any two points in a wave  measured in nm (1*10 -9 m)  Frequency ( ): the number of cycles of the wave that pass through a point in a unit of time  Measured in s -1 (per seconds) or Hz (hertz)  Speed of light (c): 3.00 x 10 8 m/s

 Baseline: midpoint between peak and trough (0 slope)  Amplitude: height of a wave  Node: point on wave where amplitude = 0

 Standing Wave: wave that has 2 or more points of no movement (confined to strict limits)  Ex. Guitar String

 5. Visible spectrum Continuous spectrum: components of white light split into its colors, ROY G BIV from 400 nm (violet) to 760 nm (red) from 400 nm (violet) to 760 nm (red)

 6.Light equation and units c = UNITS: m/s a) Longer wavelength, lower frequency b) Shorter wavelength, higher frequency Wavelength is indirectly proportional to frequency

 Ex7.1 What is the frequency of visible light with a wavelength of 625nm?

 Types of radiation from lowest to highest energy

 1.Heated objects  View in 1900 was two fold: Matter was particulate (having mass and position) Energy was waves (having no mass or fixed position) Then came Planck… Planck studied the relationship between temperature and the radiation emitted by an object. Temperature  Energy emitted

 2.Planck’s hypothesis and equation  As temperature increased molecular vibrations increased (frequency increased)  He noted that each time the temperature was increased the frequency of the radiation emitted increased in a regular increment.  Thus, he proposed that Energy was QUANTIZED.  E = h  h= x J s “Continuous” “Quantized”

 3. Ex7.2 Green light has a wavelength of 500nm. What is the energy in joules of one photon of green light? What is the energy of one mole of photons of this green light?

 4.Photoelectric effect – Nobel Prize in Physics 1921 to Albert Einstein  a. Description e- are ejected from the surface of a metal once a threshold frequency is passed  b. Practical Uses Solar Cells e- are promoted from valence band to the conduction band in a semiconductor

 c. Conclusion E photon =h ν =hc/ λ E=mc 2 or m= E/c 2 Does this mean photons have mass?  Not in the same way as other particles but they do have momentum 1. Energy is quantized. Only exists in quanta or photons. 2. Electromagnetic radiation exhibits both wave and particulate properties.

 1.Continuous vs discontinuous spectra  Continuous: shows all possible wavelengths (energies)  Discontinuous: omits 1 or more possible wavelengths

 2.Bright line, or atomic emission spectra  Light is broken down into component pieces by a diffraction grating  Only SPECIFIC ‘s of light are shown for an element  Atomic Fingerprint (distinct for each element)

 3.Bohr Model  e- rotate around nucleus in specific orbits  Energy is QUANTIZED (distinct energy levels)  Put in E  e- goes to a higher orbit  Falls back down to lower orbit  gives off E put in

 4.Energy of electrons in the ground state  Minimum amount of energy (not zero); closest to nucleus  5.Electrons in the excited state  Higher energy (further from nucleus)  6.Atomic emission spectra caused by  Electrons coming from excited to ground state which gives off a photon of light (h  )

 7.Energy of electrons is quantized  Explains why only certain wavelengths of light are shown for elements  Don’t see a continuous spectrum for hydrogen because there are not orbits for every possible wavelength

 8. Flaw in the Bohr Model  Didn’t work for elements more complex than hydrogen  Bottom Line: Bohr’s model FAILED! Fundamental Physics--A charged body (ie. an electron) following a circular orbit will emit energy and as energy decreases so does the distance to the nucleus. Thus as the electron orbits it will get closer and closer to the nucleus and the atom will eventually collapse.

 1.Wave Particle Duality – Louis deBroglie  De Broglie wondered if waves exhibit particulate properties, then do particles exhibit wave properties?

 2.Equation and “matter waves”  DeBroglie related mass (m), velocity (v), and wavelength ( ) of matter  Most matter has undetectable wavelengths  Led to the development of the electron microscope

 3.Basic idea of Quantum Theory  All matter exhibits wave and particle properties.  For very small pieces of matter (photons) wave properties dominate as they are very small particles.  For large pieces of matter (baseballs) particulate properties dominate as associated wavelengths are so small they are basically not observed.  For intermediate pieces of matter (electrons) a truly dual nature is displayed.

 1.Heisenberg Uncertainty Principle  There is a fundamental limitation to just how precisely we can know both the position and momentum of a particle at a given time. In layman’s terms: The more precisely we know a particles position the less we know about its momentum and vice versa.

 2.Schroedinger Equation’s major conclusion  A precise location for an electron cannot be determined however regions which describe the probable location for electrons can be and these regions are known as orbitals.

 a.wave functions (  )  Mathematical function that describes the location of the electron at a given moment in time  b.electron density  Shows most probable regions to find e-

 c.orbitals  3-D shape of the e- probability region (>90% e- density)   2 = probability region  d.solutions to equation  Mathematical function that satisfies the equation  Can have multiple solutions = multiple orbitals

 Quantum Numbers: mathematical way to represent the location of an electron in an atom  Analogy... State = energy level, n City = sublevel, (“L”) Address = orbital, m House Number = spin, m s

 e.Principal Quantum Number  “n”  Positive integer  Analogous to Bohr’s energy levels (and periods on the Periodic Table)  Larger n value, larger atomic size

 f.Angular Momentum Quantum Number  “ ” (small-case L)  Positive integer  within an energy level=sublevel  = 0 = s, spherical shape  = 1 = p, dumbbell shape  = 2 = d, clover shape  = 3 = f, flower shape  n=2 has 2 values (0 and 1 or s and p)  n=4 has 4 values (0,1,2,3 or s,p,d,f)

 g.Magnetic Quantum Number  “m  ”  Integer from - to +  orbital  =0 (s): m =0; 1orbital  =1 (p): m =-1,0,1; 3 orbitals  =2 (d): m =-2,-1,0,1,2; 5 orbitals

h. Spin Quantum Number  “m s ”  +½ or -½  2 electrons allowed in each orbital  “Spins” of each electron must be opposite

 3.Allowable values for quantum numbers  Correspond to solutions to the Schroedinger equation Cannot find an e- where there is no electron density  Must determine whether or not a set of quantum numbers is plausible

 4.Array of quantum numbers  Determine which of the following are Plausible:  n = 3 = 2 m = -1 m s = +½  n = 1 = 1 m = -1 m s = +½  n = 5 = 0 m = -1 m s = -½  n = 2 = 1 m = 0 m s = 0  n = 3 = 2 m = -2 m s = -½  n = 4 = 3 m = 2 m s = -½

 See back of your Packet!  1.s orbital  2.p orbital  3.d orbital  4.f orbital