Ch 6 The Structure of Atoms 6 1 Electromagnetic Radiation Electromagnetic Radiation or Light is composed of two orthogonal vectors An electric wave and a magnetic wave Vibrating electric and magnetic fields at right angles to each other 1 The wavelength of EM radiation has the symbol Wavelength is the distance from the top crest of one wave to the top of the next wave Measured in units of distance such as m cm nm etc 1 1 x 10 10 m 1 x 10 8 cm 2 The frequency of electromagnetic radiation has the symbol Frequency is the number of crests or troughs that pass a given point per second like water waves hitting the pier Measured in units of 1 time 1 s s 1 Hertz l speed of propagation of the wave or c for light c speed of light 3 00 x 108m s in a vacuum speed of light for all is the same Wavelength and frequency are inversely proportional to each other for the same wave shorter wavelengths correspond to higher frequency 3 Electromagnetic Radiation The relationship between wavelength and frequency for any wave is velocity For electromagnetic radiation the velocity is 3 00 x 108 m s and has the symbol c Thus c for electromagnetic radiation UV shorter higher IR longer low High Energy High Frequency Short or Low Energy Low Frequency Long 4 Clicker Q Which has the highest frequency A rays B x rays C IR D long radio waves Clicker Q Which has the lowest energy 5 Clicker Q What is the frequency of green light of wavelength 5200 c for light c 3 00 x 108 m s 1 1 00 x 10 10 m Press log button then enter that number No e notation 6 6 2 Quantization Planck Einstein Energy and Photons Planck s equation E energy in Joules photon h Planck s constant 6 626 x 10 34 J s frequency units of Hertz 1 s or s 1 E h hc Light with long low has low energy E Light with short high has high energy E As the frequency of light increases the energy of the photon increases As the wavelength of light increases the energy of the photon decreases 7 UV light has a 2 73 x 1016 1 s what is its energy Clicker Q Yellow light has a 5 27 x 1014 1 s Energy Enter as e A laser having a wavelength of 508 nm emits 4 28 x 1017 photons of light per second How much energy in Joules does this laser emit in 5 00 seconds The energy of a particular color of red light is 2 92E 22 kJ What is the wavelength of this light in nanometers 10 Einstein and the Photoelectric Effect Certain metals will release eject electrons when light strikes the metal surface The energy of the light must exceed a minimum or threshold energy for this to occur Any excess energy beyond this minimum goes into the kinetic energy of the ejected electron They fly away with greater velocity A Einstein 1879 1955 Photoelectric Effect Classical theory suggests that energy of an ejected electron should increase with an increase in light intensity This however is not experimentally observed No ejected electrons were observed until light of a certain minimum energy is applied Number of electrons ejected depends on light intensity so long as the light is above a minimum energy This minimum energy is also the ionization energy of the metal Photoelectric Effect Experiment demonstrates the particle like nature of light Photoelectric Effect Conclusion There is a one to one correspondence between ejected electrons and light waves This can only occur if light consists of individual units called PHOTONS A Photon is a packet of light of discrete energy http www youtube com watch v N7BywkIretM feature related 6 3 Atomic Line Spectra and Niels Bohr An emission spectrum is formed by an electric current passing through a gas in a vacuum tube at very low pressure which causes the gas to emit light Sometimes called a bright line spectrum 15 When the light from a discharge tube containing a pure element hydrogen in this case is passed through the same prism only certain colors lines are observed Recall that color wavelength is related to energy via Planck s law Light emitted by H2 Emission spectrum of hydrogen 16 An absorption spectrum is formed by shining a beam of white light through a sample of gas Absorption spectra indicate the wavelengths of light that have been absorbed 17 Every element has a unique spectrum Thus we can use spectra to identify elements This can be done in the lab stars fireworks etc Spectra can serve as fingerprints that allow us to identify different elements present in a sample even in trace amounts 18 Balmer equation The Balmer equation 1 1 1 R 2 2 is an empirical n1 n 2 equation that relates R is the Rydberg constant the wavelengths of 7 1 R 1 097 10 m the lines in the n1 n 2 hydrogen spectrum Derived from n s refer to the numbers numerous of the energy levels in the observations not emission spectrum of hydrogen from theory 19 What is the wavelength of light emitted when the hydrogen atom s energy changes from n 4 to n 2 20 Solution What is the wavelength of light emitted when the hydrogen atom s energy changes from n 4 to n 2 n 2 4 and n1 2 1 1 1 R 2 2 l n1 n 2 1 1 097 107 m 1 l 1 1 2 2 2 4 1 1 1 7 1 1 097 10 m l 4 16 1 1 097 107 m 1 0 250 0 0625 l 1 1 097 107 m 1 0 1875 l 1 2 057 106 m 1 l 21 Notice that the wavelength calculated from the Balmer equation matches the wavelength of the green colored line in the H spectrum 22 When an electron is excited from a lower energy level to a higher one it absorbs a definite or quantized amount of energy When the electron falls back to the original energy level it emits exactly the same amount of energy it absorbed in moving from the lower to the higher energy level Draw energy levels Clicker Q Going from n 2 to n 4 is A Absorption B emission Clicker Q Which is closer to the nucleus B n 1 C n 2 D n 3 E n 4 F n 24 Fig 6 10 p 277 Long wavelength low frequency low energy transition short line on the diagram Short wavelength high frequency high energy transition long line on the diagram Absorption up Emission down Ionization goes from n 1 to 26 The Bohr Model of the Atom The energy of each level is given by En Rhc 2 n R Rydberg constant 1 097 107 m 1 h Planck s constant 6 626 10 34Js c speed of light 2 997 108 ms 1 n the quantum level of the electron 1 2 3 The sign …