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C.F. 1 MOLE : 6.02 x 1023 ATOMS Question gives you moles and asks for number of atoms Question gives you number of atoms and ask for moles C.F. 1 MOLE : Molar Mass in Grams Question gives you moles and asks for grams Question gives you grams and asks for moles C.F. Molar Mass = MOLE = 6.02 x 1023 atoms Question gives you grams and asks for number of atoms 1. Convert grams to Moles 2. Convert moles to # of atoms C.F. 6.02 x 1023 atoms = MOLE = Molar Mass Question gives you number of atoms and asks for mass in grams 1. Convert # of atoms to moles 2. Convert moles to grams INSTRUCTIONS 1. Draw sideways T 2. Write your “given” in the first box If you are given GRAMS: 1. Use Periodic Table to find molar mass of element. 2. Solve 1. Use “6.02x 1023 2. Solve If you are given # OF ATOMS atoms” INSTRUCTIONS 1. Draw sideways T 2. Write your “given” in the first box 1. 2. 3. 4. 5. 6. 7. If you are given GRAMS: Write “1 mole” in the next top box. Then write the molar mass in the opposite corner. Solve for mole. Convert mole to number of atoms by: Write “6.02 x 1023 atoms” in the next top box Then write “1 mole” in the opposite corner Solve INSTRUCTIONS 1. Draw sideways T 2. Write your “given” in the first box 1. 2. 3. 4. 5. 6. If you are given GRAMS: Find molar mass using periodic table and write in the opposite corner. Write “1 mole” in the box above. Convert mole to number of atoms by: Then write “1 mole” in the opposite corner Write “6.02 x 1023 atoms” in the box above Solve If you are given # OF ATOMS 1. 2. 3. 4. 5. 6. Then write “6.02x 1023 atoms” in the opposite corner. Write “1 mole” in the box above. Convert mole to grams by: Then write “1 mole” in the opposite corner. Find molar mass using periodic table and write it in the box above Solve 1. Quantum Model of the Atom OBJECTIVE: To understand energy, and how we got to our present understanding of an atom 1. Quantum Model 1. Quantum Model Wavelength: distance between two points, either crests or troughs 1. Quantum Model Frequency: number of waves that passes a certain point in 1 second. 1. Quantum Model 2 properties of waves Wavelength: distance between two points, either crests or troughs Symbol: l Units = meters, m Frequency: How many waves that passes a certain point in 1 second. Symbol: v Units = Hz, or sec-1 INVERSE relationship between wavelength and frequency 1. Quantum Model 2 properties of waves Wavelength: is… Symbol: ? Units = ? Frequency: is… Symbol: ? Units = ? What does it mean for wavelength and frequency to have an inverse relationship? 1. Quantum Model Calculations using lv = c A wave has a frequency of 4.61 x 104 Hz. What is its wavelength in meters? 1. 2. 3. 4. Write the equation: lv = c Plug in values. C = 3.0 x 108 m/s ALWAYS Rearrange equation to solve for unknown. Solve 1. Quantum Model Calculations using lv = c Your favorite radio station broadcasts the signal at 99.5 MHz. This is equal to 9.96 x 107 Hz. Calculate the wavelength in meters. 1. 2. 3. 4. Write the equation: lv = c Plug in values. C = 3.0 x 108 m/s ALWAYS Rearrange equation to solve for unknown. Solve 1. Quantum Model Calculations using lv = c Photosynthesis uses light waves with a wavelength of 660 nm to convert CO2 and H2O into glucose and O2. 660 nm = 6.6 x 10-7m Calculate the frequency. 1. 2. 3. 4. Write the equation: lv = c Plug in values. C = 3.0 x 108 m/s ALWAYS Rearrange equation to solve for unknown. Solve 1. Quantum Model Answer on Warmup Paper. Label it as “WAVES” Wavelength Frequency What is… Symbol: Unit: Your favorite FM radio station broadcasts at a frequency of 101.1 MHz. This is equal to 1.011 x 108 Hz. What is the wavelength of this station in meters? A police officer is using a radar gun for speeding citations. The gun uses waves with a wavelength of 8.45 nanometers. This is equal to 8.45 x 10-9 meters. What is the frequency in Hz? 1. Quantum Model Calculations using lv = c Photosynthesis uses light waves with a wavelength of 660 nm to convert CO2 and H2O into glucose and O2. 1 nm = 1.0 x 10-9m. Calculate the frequency. 1. 2. 3. 4. 5. Convert 660nm to meters using sideways-T Write the equation: lv = c Plug in values. C = 3.0 x 108 m/s ALWAYS Rearrange equation to solve for unknown. Solve 1. Make sure that l is in METERS, or that v is in Hz 2. If not, then convert to METERS or Hz using the conversion factors given to you. 3. Solve: Step-by-step instructions on how to solve should be in your notes 4. Does your final answer have the units that is asked for in the problem? 1. Quantum Model 1. Quantum Model X-Ray Sunburn from UV rays 1. Quantum Model Heat energy in the form of Infrared waves 1. Quantum Model In the 1900’s physicist thought they were able to explain any type of phenomena. They organized the world into two categories: Matter - Made up of particles Energy - Energy, in the form of light, existed as waves 1. Quantum Model In the 1900’s physicist thought they were able to explain any type of phenomena. They organized the world into two categories: Matter -Made up of particles - Has mass and volume Energy -Energy, in the form of light, existed as waves - does NOT have mass or volume 1. Quantum Model Energy as massless waves 1. Quantum Model Relationship between ENERGY and WAVELENGTH 1. Quantum Model 1. Quantum Model Quantized? Max Plank Means that energy is gained or lost ONLY in amounts of WHOLE NUMBERS Means that energy is transferred in “packages” called a QUANTUM = the smallest unit of energy Similar Examples: 1. Musical instruments are “quantized” in that they can only produce certain notes, like C or F#. 2. US Dollars is “quantized” in whole number multiples of pennies. 1. Quantum Model What does it mean for energy to be QUANTIZED? What is a quantum? How is a penny like a quantum? 1. Quantum Model Max Plank E = hv 1. Quantum Model Einstein and the Photoelectric Effect Photoelectric Effect: when electrons are released from a surface of a metal that has been exposed to light 1. Quantum Model Einstein and the Photoelectric Effect Why does nothing happen when red light makes contact with the metal? Why does only violet light release an electron? 1. Quantum Model Einstein and the Photoelectric Effect It was thought that color should not matter, only intensity But experiment showed that color does matter. 1. Quantum Model Einstein and the Photoelectric Effect Einstein applied Plank’s idea, that…, to the photoelectric effect… 1. Quantum Model Einstein and the Photoelectric Effect Light is also quantized Light is a stream of particles called PHOTONS PHOTON: a particle of light 1. Quantum Model Why Plank and Einstein are important 1. Quantum Model Why Plank and Einstein are important Plank’s and Einstein's postulate that energy is quantized is in many ways similar to Dalton’s description of atoms. Both theories are based on the existence of simple building blocks, atoms in one case, and quanta in the other. The work of Plank and Einstein thus suggested a connection between the quantized nature of energy and the properties of individual atoms. In fact, Einstein's Nobel Prize was awarded for his work in the photoelectric effect and demonstrating its fundamental important, not for his famous E=mc2 equation. 1. Quantum Model Summary of Plank and Einstien 1. Energy is quantized. It can only occur in discrete units called quanta. 2. Light, in fact the entire electromagnetic spectrum, exists as BOTH waves and particles. Interesting Implications – What their findings mean 1. Energy has “mass!” 2. If it has mass, then energy is a form of matter! 3. If energy, in the form of light, is both wave and particle, then ALL MATTER exists as both waves and particles 1. Quantum Model In the 1900’s physicist organized the world into two categories: Matter -Made up of particles - Has mass and volume Energy -Energy, in the form of light, existed as waves - does NOT have mass or volume But after Plank and Einstein’s work, we now see that ENERGY (light) and MATTER NOT separate, but related 1. Quantum Model What does it mean for light to be quantized? What is a photon? What is a quantum? How is a photon like a quantum? 1. Quantum Model 1. Quantum Model 1. Quantum Model 1. Quantum Model 1. Quantum Model What does it mean for energy to be quantized? What does it mean for light to be quantized? What is a quantum? What is a photon? How is a penny or steps on a stair like a quantum of energy? 1. Quantum Model Plank + Einstein = Calculating the Energy of one Photon E = (hc)/l 1. Quantum Model Plank + Einstein = Calculating the Energy of one Photon E = (hc)/l h = Plank’s Constant h = 6.626 x 10-34 J•sec This number NEVER changes (J = Joule, the unit for measuring energy) 1. Quantum Model Plank + Einstein = Calculating the Energy of a Photon E = (hc)/l The blue color in fireworks results when copper is heated to about 1200°C. The blue light has a wavelength of 450 nm. What is the unit of energy emitted? 1. Write equation 2. Plug in values. h = 6.626 x 10-34 J•sec ALWAYS 3. Solve ANSWER = 4.42 x 10-19 J 1. Quantum Model Plank + Einstein = Calculating the Energy of a Photon E = (hc)/l A ruby laser used at grocery stores to scan barcodes emits a red light at a wavelength of 694.3 nm. What is the energy in J? 1 nm = 1.0 x 10-9 m 1. Write equation 2. Make sure l is in METERS. Plug in values. h = 6.626 x 10-34 J•sec ALWAYS 3. Plug in values. h = 6.626 x 10-34 J•sec ALWAYS 4. Solve 1. Quantum Model Plank + Einstein = Calculating the Energy of a Photon E = (hc)/l A ruby laser emits a red light at a wavelength of 694.3 nm. What is the energy in J? 1. Write equation 2. Make sure l is in METERS. Plug in values. h = 6.626 x 10-34 J•sec ALWAYS 3. Plug in values. h = 6.626 x 10-34 J•sec ALWAYS 4. Solve ANSWER = 2.861 x 10-19 J 1. Quantum Model Plank + Einstein = Calculating the Energy of a Photon E = (hc)/l An x-ray generator, such as those used in hospitals, emits radiation with a wavelength of 1.544 angstrom. What is the energy of a single proton? 1. Write equation 2. Make sure l is in METERS. Plug in values. h = 6.626 x 10-34 J•sec ALWAYS 3. Plug in values. h = 6.626 x 10-34 J•sec ALWAYS 4. Solve 1. Quantum Model Plank + Einstein = Calculating the Energy of a Photon E = (hc)/l 1. Write equation 2. Make sure l is in METERS. If not, then convert it to METERS using sideways T 3. Plug in values h = 6.626 x 10-34 J•sec ALWAYS Plug in values. c = 3.0 x 108 m/sec ALWAYS 4. Solve 1. Quantum Model Energy, Photons and Line Spectrum 1. Quantum Model Energy, Photons and Line Spectrum What is a line spectra? Normal, white light, separates into all the colors of the visible spectrum. 1. Quantum Model Energy, Photons and Line Spectrum What is a line spectra? When PURE elements are heated using an electric charge, they give off light. But when that light passes Through a prism, only a few narrow lines of color are seen. 1. Quantum Model Energy, Photons and Line Spectrum What is a line spectra? When PURE elements are heated using an electric charge, they give off light. But when that light passes Through a prism, only a few narrow lines of color are seen. 1. Quantum Model Energy, Photons and Line Spectrum What is a line spectra? Line Spectrum = a spectrum in which light of only certain wavelength is emitted or absorbed, rather than a continuous range of wavelengths. 1. Quantum Model Energy, Photons and Line Spectrum What is a line spectra? 1. Quantum Model Energy, Photons and Line Spectrum Why do we get line spectrums? Neil Bohr said it is because atoms have energy levels that are QUANTIZED 1. Quantum Model Bohr’s Model 1. Quantum Model Bohr’s Model Bohr said that electrons ORBIT the nucleus Okay…how is this different from Rutherford’s model? 1. Quantum Model Bohr’s Model Bohr said that electrons ORBIT the nucleus, and that these orbits OCCUPY ONLY CERTAIN REGIONS OF SPACE ORBITS are QUANTIZED The ORBITS represent different energy levels These energy levels are quantized 1. Quantum Model Bohr’s Model 1. Quantum Model Bohr’s Model Ground State = when electrons are arranged in the most stable and lowest possible energy level. Ground State has a value of n = 1 EXAMPLE: Standing on the lowest step 1. Quantum Model Bohr’s Model Excited State = when electrons are arranged with a higher energy level than the ground state. Not as stable as ground state. Excited State has a value of n EXAMPLE: standing on any step higher than the first one >1 1. Quantum Model Bohr’s Model Excited State = when electrons are arranged with a higher energy level than the ground state. Not as stable as ground state. Excited State has a value of n >1 HIGHER the N number, the more unstable 1. Quantum Model Bohr’s Model 1. Quantum Model Bohr’s Model 1. Quantum Model Bohr’s Model 1. Quantum Model Bohr’s Model 1. Quantum Model Bohr’s Model 1. Quantum Model Bohr’s Model 1. Quantum Model Bohr’s Model 1. Quantum Model Bohr’s Model 1. Quantum Model Just like you must be ON a step and not in between steps, electrons must also be ON a step. These steps are like _____ levels, and Bohr called these energy levels ______. Bohr said these orbits are ______ because electrons will always be located in an orbit, never between. The lowest step on stairs is like the _____ state, and any step that is higher is like the _____ state. When you jump off a step close to the ground, you make little noise. This is like red light that has a long wavelength, a ____ frequency and not much _____. When you jump off a step that is very high, and jump to the ground, you make a loud noise. This is like violet light that has a shorter wavelength, a _____ frequency, and so lots of ______. Orbits 1. represent… Orbits are quantized, meaning… ENTER ANSWER Quantum HERE Model Bohr’s Model ENTER RESPONSE HERE Ground state = ENTER ANSWER HERE n ? 1 Excited state = ENTER RESPONSE HERE n ? 1 1. Quantum Model Bohr’s Model 3. Describe what happens when the electron falls from an excited state to a ground state? When an electron falls from an excited state to the ground state, light is emitted. The color of light depends on the change in energy levels, just like the sound made when jumping off stairs. Jumping off a high step makes a loud noise and has a high frequency with high energy. Like Jenga, the higher the block, the more sound it produces. 1. Quantum Model Bohr’s Model 4. How does the above explain why elements have line spectrum and not a continuous spectrum? Elements have line spectrums instead of a continuous spectrum because the orbits are quantized, which means there are gaps from which electrons cannot fall. The lines represent the color that go with the amount of energy. It can only be a continuous spectrum if the electron is able to move without the orbits 1. Quantum Model Bohr’s Model 5. How is this related to fireworks? 1. Quantum Model Bohr’s Model Main importance of Bohr’s Model His main contribution: There is a connection between the orbits of an atom and its line spectrum. But why are orbits only at certain levels? 1. Quantum Model De Broglie and Standing Waves But why are orbits only at certain levels? De Broglie hypothesized that the electron behaves like a standing wave 1. Quantum Model De Broglie and Standing Waves standing wave = a wave that does not travel An example = a string of a violin or guitar. When the string is plucked, it vibrates at certain fixed frequencies because it is fastened at both ends. 1. Quantum Model De Broglie and Standing Waves standing wave = a wave that does not travel NOT standing waves 1. Quantum Model De Broglie and Standing Waves standing wave = a wave that does not travel 1. Quantum Model De Broglie’s idea that an electron is a s______ w____ explained Bohr’s orbits and energy levels nicely How? visual demo 1. Quantum Model De Broglie’s idea that an electron is a s______ w____ explained Bohr’s orbits and energy levels nicely How? 1. Quantum Model De Broglie’s idea explained Bohr’s orbits and energy levels nicely lowest energy level, n = 1 one complete wavelength would close the circle 2πr = nλ Higher energy levels would have successively higher values of n with a corresponding number of nodes. n = number of nodes 1. Quantum Model 1. Quantum Model ONE PROBLEM with De Broglie’s idea: Because a wave is a disturbance that travels in space, it has no fixed position. One might therefore expect that it would also be hard to specify the exact position of a particle that exhibits wavelike behavior. 1. Quantum Model ONE PROBLEM with De Broglie’s idea: Hard to know exactly where the wave/particle is AND how fast it is moving German physicist Werner Heisenberg Uncertainty Principle: We can know position/WHERE an electron is OR momentum/SPEED NOT BOTH 1. Quantum Model So where is an electron? We do not know! If we know where it is, we do not know how fast it is going If we know how fast it is going, we do not know where it is CANNOT KNOW BOTH 1. Quantum Model CANNOT KNOW BOTH The best we can do is… it is probably here OR it is probably going this fast 1. Quantum Model Erwin Schrodinger 1. Quantum Model Erwin Schrodinger Plank + Einstein + Bohr + De Broglie + Heisenberg = Schrodinger’s Quantum Model of the atom = 1. Quantum Model Erwin Schrodinger Plank + Einstein + Bohr + De Broglie + Heisenberg = Schrodinger’s Quantum Model of the atom Last model of the atom we will learn!! 1. Quantum Model Erwin Schrodinger Schrodinger’s Quantum Model of the atom = Model that shows where electrons (as both a wave and a particle) probably are in an atom 1. Quantum Model Erwin Schrodinger Quantum Numbers 1. Quantum Model Erwin Schrodinger Quantum Numbers 4 numbers that tells us where electrons most likely are 1. Quantum Model QUANTUM NUMBERS 1. The Principal Quantum Number 1. Quantum Model QUANTUM NUMBERS 1. The Principal Quantum Number The principal quantum number (n) tells the average distance of an electron from the nucleus: 1. Quantum Model QUANTUM NUMBERS 1. The Principal Quantum Number The principal quantum number (n) tells the average distance of an electron from the nucleus: n = 1, 2, 3, 4,… 1. Quantum Model QUANTUM NUMBERS 2. The Angular Quantum Number describes shape of space where electrons most likely are. The values of l = 0 to n − 1 1. Quantum Model QUANTUM NUMBERS 2. The Angular Quantum Number describes shape of space where electrons most likely are. The values of EX: n = 1 l = 0 to n − 1: 1. Quantum Model QUANTUM NUMBERS 2. The Angular Quantum Number describes shape of space where electrons most likely are. The values of l EX: n = 1, 1-n=0 So l = 0 = 0 to n − 1: n=2 1-n=1 So l = 0, 1 n=3 1-n=2 So l = 0, 1, 2 1. Quantum Model The Magnetic Quantum Number The third quantum number is the magnetic quantum number (ml). The value of ml describes the orientation of the region in space occupied by an electron with respect to an applied magnetic field. The allowed values of ml depend on the value of l: ml can range from −l to l in integral steps: EQUATION 6.23 ml = −l, −l + 1,…, 0,…, l − 1, lv 1. Quantum Model QUANTUM NUMBERS 2. The Angular Quantum Number describes shape of space where electrons most likely are. The values of l EX: n = 1, 1-n=0 So l = 0 = 0 to n − 1: n=2 1-n=1 So l = 0, 1 n=3 1-n=2 So l = 0, 1, 2 1. Quantum Model What is the difference between an ORBIT and an ORBITAL? An orbit is the exact path an electron travels. An ORBITAL is a 1. Quantum Model What is the difference between an ORBIT and an ORBITAL? 1. Quantum Model Because a wave is a disturbance that travels in space, it has no fixed position. One might therefore expect that it would also be hard to specify the exact position of a particle that exhibits wavelike behavior. This situation was described mathematically by the German physicist Werner Heisenberg 1. Quantum Model the wavelike nature of subatomic particles such as the electron made it impossible to use the equations of classical physics to describe the motion of electrons in atoms. Scientists needed a new approach that took the wave behavior of the electron into account. In 1926, an Austrian physicist, Erwin Schrödinger (1887–1961; Nobel Prize in Physics, 1933), developed wave mechanics, a mathematical technique that describes the relationship between the motion of a particle that exhibits wavelike properties (such as an electron) and its allowed energies. In doing so, Schrödinger developed the theory of quantum mechanics, describe the energies and spatial distributions of electrons in atoms and molecules. 1. Quantum Model As n increases for a given atom, so does the average distance of an electron from the nucleus. A negatively charged electron that is, on average, closer to the positively charged nucleus is attracted to the nucleus more strongly than an electron that is farther out in space. This means that electrons with higher values of n are easier to remove from an atom. All wave functions that have the same value of n are said to constitute a principal shell because those electrons have similar average distances from the nucleus. As you will see, the principal quantum number n corresponds to the n used by Bohr 1. Quantum Model The Azimuthal Quantum Number For example, if n = 1, l can be only 0; if n = 2, l can be 0 or 1; and so forth. For a given atom, all wave functions that have the same values of both n and l form a subshell. The regions of space occupied by electrons in the same subshell usually have the same shape, but they are oriented differently in space. 1. Quantum Model For example, if l = 0, ml can be only 0; if l = 1, ml can be −1, 0, or +1; and if l = 2, ml can be −2, −1, 0, +1, or +2. Each wave function with an allowed combination of n, l, and ml values describes an atomic orbital,