Chem102 9.30 - Chemistry 102B Discussion Worksheet#9...

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Unformatted text preview: Chemistry 102B Discussion Worksheet #9 Electromagnetic Radiation and the Bohr Model Electromagnetic Radiation (light) is known to have the wave-like properties of frequency () and wavelength (). The distance between two peaks is called the wavelength and the number of waves per unit time (1 second typically) is called the number of cycles or the frequency (cycles/s or Hz). As the frequency increases, the wavelength decreases. Frequency and wavelength are related through the following equation: c = Where c = speed of light in a vacuum, 2.998 x 108 m/s, = wavelength (m) and = frequency (s-1 or Hz). The electromagnetic radiation spectrum is shown below. ACTION ITEMS Which radiation has wavelengths longer than visible light? 1 1. The wavelength of green light is approximately 522 nm. What is the frequency of this radiation? 2. What is the wavelength of a photon that has a frequency of 2.10 x 1014 Hz? Answer in nm and determine what type of radiation this corresponds to (from EMR spectrum). Planck recognized that energy is quantized and related the energy of radiation (emitted or absorbed) to its frequency. E = nh = nhc/ where n = integer and h = Planck's constant = 6.626 x 10-34Js ACTION ITEMS 3. Categorize the relationship as being direct or inverse for the following: a. energy and wavelength b. wavelength and frequency c. frequency and energy 4. A classical radio station broadcasts at 93.5 MHz (M = 106). Find the wavelength of this radiation, in meters, and then energy of the photons, in J. What type of radiation is this? 2 Bohr applied this concept to line spectra of elements. When elements are excited they emit radiation at fixed wavelengths. He proposed that only certain energy levels are allowed within the structure of the atom. Electrons are allowed to move between those energy levels by absorbing or emitting photons of light. The light emitted by the elements is a measure of the energy gap between two electronic states. For the hydrogen atom: E = -RH Z2(1/nf2 1/ni2) RH = Rydberg constant = 2.178 x 10-18 J, Z = nuclear charge = 1 for H, 2 for He etc. ACTION ITEMS 5. Calculate the E for the n = 4 to the n = 2 transition in hydrogen. Where on the EMR spectrum would this appear? What does the sign mean? 6. A hydrogen atom in its ground state absorbs light with a wavelength of 102.6 nm. Calculate the energy level of the resulting excited state (n = ?). 3 Ionization Energy is the energy required to completely remove an electron from an atom. This can be thought of as a transition between n =1 and n = . ACTION ITEMS 7. Calculate the energy needed to remove the electron from hydrogen in its ground state. This is the energy to remove an electron from the ground state of hydrogen. What wavelength of light would work? What type of radiation does this correspond to on EMR spectrum? 8. What is the energy needed to remove the remaining electron from He+ in its ground state? Is it easier or more difficult to remove an electron from He+ or H? 4 ...
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