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Topic 3. Atomic Structure and Electron Configuration. Light. Is a form of electromagnetic radiation. Waves of electric and magnetic fields at right angles to each other. Parts of a wave. Wavelength. l. Frequency = number of cycles in one second
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Topic 3 Atomic Structure and Electron Configuration
Light • Is a form of electromagnetic radiation. • Waves of electric and magnetic fields at right angles to each other.
Parts of a wave Wavelength l Frequency = number of cycles in one second Measured in hertz 1 hertz = 1 cycle/second (s-1)
Frequency = n As frequency increases the wavelength decreases (inversely related)
Kinds of EM waves • There are many kinds of electromagnetic waves • They have different wavelengths (l) and frequencies (n) • Radio waves, microwaves, x rays and gamma rays are all examples. • Light is only the part our eyes can detect. G a m m a R a d i o w a v e s R a y s Short Wavelengths High Energy Long Wavelengths Low Energy
The speed of light • Speed of light = c • The speed of light in a vacuum is c = 2.998 x 108 m/s c = ln 1. What is the wavelength of light with a frequency 5.89 x 105 Hz? 2. What is the frequency of blue light with a wavelength of 484 nm?
In 1900 • Matter and energy were seen as different from each other in fundamental ways. • Matter was made of particles and had mass. • Had mass and position could be specified • Energy was described as a wave with any frequency. • was massless and delocalized – position in space could not be specified • Max Planck found that the cooling of hot objects couldn’t be explained by viewing energy as a wave.
Energy is Quantized • Planck found DE (energy lost as the metal cooled) came in specific quantities with size hn • DE = nhn • where n is an integer. • and h is Planck’s constant • h = 6.626 x 10-34 J s • these packets of hn are called quantum
Ex. 7.2 • The blue color in fireworks is often achieved by heating copper (I) chloride (CuCl) to about 1200oC. Then the compound emits blue light having a wavelength of 450 nm. What is the increment of energy (the quantum) that is emitted at 4.50 x 102 nm by CuCl?
Einstein and photons • Einstein said electromagnetic radiation is quantized in particles called photons. • Each photon has energy = hn = hc/l • Combine this with E = mc2 • You get the apparent mass of a photon. • m = h / lc
Summary • Energy is quantized. It can occur only in discrete units called quanta. • Electromagnetic radiation, which was previously thought to exhibit only wave properties, seems to show certain characteristics of particulate matter as well. • This is referred to as the “dual nature of light.”
Matter as a wave • Recall previously that m = h/lc. • Using the velocity v instead of the speed of light “c” and solving for wavlength l we get • De Broglie’s equation l = h/mv • We can calculate the wavelength of an object.
Diffraction Patterns: Evidence of Wave Properties • When light passes through, or reflects off, a series of thinly spaced line, it creates a rainbow effect because the waves interfere with each other.
Two Curves with two holes
Two Curves with two holes Interfere with each other
Two Curves with two holes Interfere with each other crests add up
Several waves Several Curves
Several waves Several waves Several Curves Interference Pattern
What will an electron do? • It has mass, so it is matter. • A particle can only go through one hole. • A wave through both holes. • An electron does go though both, and makes an interference pattern. • It behaves like a wave. • Other matter has wavelengths too short to notice.
Spectrums of light • The range of frequencies present in white light is continuous. • All the colors are possible. • We see a complete rainbow (ROYGBIV).
Hydrogen spectrum • Called an emission spectrum because these are the colors it gives off or emits. • Each color corresponds to a certain amount (or quanta) of energy given off. • This is called a line spectrum. • There are just a few discrete lines showing – not a continuous spectrum. Why? 656 nm 434 nm 410 nm 486 nm
What a line spectrum indicates • Only certain energies are allowed for the hydrogen atom. (If any energy were allowed we would see a continuous spectrum) • Use DE = hn = hc / l • Energy in the in the atom is quantized.
Niels Bohr • Bohr explained the hydrogen emission spectrum by developing the quantum model of the hydrogen atom. • He said the atom was like a solar system. • The electrons were attracted to the nucleus because of opposite charges.
The Bohr Ring Atom • He didn’t know why but only certain energies were allowed. • He called these allowed energies – “energy levels”. • Putting Energy into the atom moved the electron away from the nucleus. (from ground state to excited state) • When it returns to ground state it gives off light of a certain energy.
The Bohr Ring Atom n = 4 n = 3 n = 2 n = 1
The Bohr Model • The energy of an electron at a specific energy level is calculated using the Rydberg equation: • E = -2.178 x 10-18J (Z2 / n2 ) • n = the energy level • Z is the nuclear charge, which is +1 for hydrogen. • n = 1 is called the ground state • when the electron is removed, n = ¥ • E = 0
We can calculate energy change of an electron in Hydrogen • When the electron moves from one energy level to another. • DE = Efinal- Einitial • DE = -2.178 x 10-18J (1/ nf2 - 1/ ni2)
When does Bohr’s model work? • Only for hydrogen atoms and other monoelectronic species. • Why the negative sign? • The maximum energy an electron can have is zero, at an infinite distance. • The closer the electron is to the nucleus the lower the energy of the electron (and therefore more stable).
The Bohr Model • Only works for the hydrogen atom. It doesn’t work for other atoms. • Electrons don’t move in circles (orbits). • The quantization of energy is right, but not because they are circling like planets.
The Quantum Mechanical Model • A totally new approach. • De Broglie said matter could be like a wave, specifically standing waves. • Like the vibrations of a stringed instrument.
What’s possible? • Electrons can be described as standing waves in an atom. • There must be an exact number of half or whole waves, so only certain wavelengths can exist. • These correspond to specific energies of the electrons.
Schrodinger’s Equation • 1925 Erwin Schrodinger described the wave function of the electron. • The equation and math are complicated, but what is important are the solutions. • Solutions to the equation are called orbitals. (These are not Bohr orbits.) • Each solution: 1. Indicates the probability of where an electron can be found 2. is tied to a certain energy or energy level.
The “probability” suggests: • There is a limit to what we can know about an electron • We can’t know how the electron is moving or how it gets from one energy level to another. • The Heisenberg Uncertainty Principle. • There is a limit to how well we can know both the position and the momentum of an object.
The Heisenberg Uncertainty Principle expressed mathematically: • Dx · D(mv) ≥ h/4p • Dx is the uncertainty in the position. • D(mv) is the uncertainty in the momentum. • the minimum uncertainty is h/4p
What does the wave Function mean? • Nothing - it is not possible to visually map it. • The square of the function is the probability of finding an electron near a particular spot. • The best way to visualize it is by mapping the places where the electron is likely to be found.
Probability Distance from nucleus
Sum of all Probabilities Distance from nucleus
Defining the orbital • The size or space that encloses 90% to the total electron probability. • (You can think of it as a space where the electron can be found 90% of the time.) • For the first solution the shape of the orbital is a a sphere.
Quantum Numbers • There are many solutions to Schrodinger’s equation • Each solution can be described with four quantum numbers that describe some aspect of the solution. • (1) Principal quantum number (n) is the size and energy of an orbital.
Quantum numbers • (2) Angular momentum quantum number (l) is the shape of the orbital. • called s, p, d, or f • Beyond f they are alphabetical g, h, …
