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Transcript
Max Planck (1858 – 1947) Founder of the quantum theory Proposed that radiation is emitted in discreet packets called quanta (singular quantum) Energies associated with these quanta are proportional to the frequencies of the emitted radiation. He formulated the following equation: E = hf Where E is the energy of radiation h is Planck’s constant (6.626 x 10-34 Js) f is the frequency of the radiation. Albert Einstein (1879 – 1955) Theory of relativity Theory of the photoelectric effect – Noble prize in 1921 The photoelectric effect Einstein viewed electromagnetic radiation as beams of photons – each photon is a little packet of energy with the value E = h f. Frequency is equal to the speed of light divided by the wavelength of the radiation in question and thus this equation can be rearranged to read: E=hc Using this equation he set about trying to explain why high frequencies of photons, whereas they caused more electrons to be ejected from the surface of the solid, did not change the energy each electron possessed. This equation, which uses the principle of the law of conservation of energy, won Einstein his noble prize. Note: The theories of Planck and Einstein were the first steps in the development of the quantum theory. Louis DeBroglie French physicist Received the Nobel Prize in physics in 1929. Louis de Broglie proposed the wave-particle duality of light. This simply put, is the phenomenon that waves behave both like a particle and as a wave. De Broglie proposed that both light and matter obey the equation: = h mv Where: λ is the de Broglie wavelength m is the mass which when multiplied by velocity is momentum h is Planck’s constant Sample problem: Calculate the de Broglie wavelength of an electron traveling at a speed of 3.0 x 106 m/s ( 1 % the speed of light). v = 3.0 x 106 m/s m = 9.11 x 10-31 Kg h = 6.626 x 10-34 J s Note: The wavelength of the electron falls in the X-ray region of the electromagnetic spectrum. (1 x 10-9 m = 1 nanometer) Neils Bohr 1885 - 1962 Danish physicist First quantum model of the atom Formulated a description of the hydrogen atom that explained its light spectra Using Einstein’s work and Planck’s work – Bohr related the colour of hydrogen’s spectra to wavelength and then wavelength to energy. Bohr postulated that the colours of the Hydrogen spectra were discreet bands of colour – the photons causing the electrons to be released when excited electrons drop back from higher energy levels at which they exist. Bohr showed that electrons are quantized. He demonstrated that the only possible energies of electrons in his orbital/energy levels would be given by the equation: En = - 1311 KJ/mol n2 The En values given by this equation corresponds to the energy states of electrons in a hydrogen atom. These stationary states/energy levels are known as the ground state and excited states. The Hydrogen Spectrum of Light When an electron makes a transition form a higher energy state to a lower energy state each transition is accompanied by the emission of a photon having a wavelength that corresponds with the electromagnetic spectrum. Radio waves, microwaves, infrared light, visible light, ultraviolet light, X-rays and gamma rays are all forms of electromagnetic radiation. When electrons are passed through a gas, radiation is emitted at discreet wavelengths. This is called a line spectrum. If we are examining a gas consisting of individual atoms then we call the spectra atomic emission spectra. In 1885 Johann Balmer – an amateur Swiss scientist – developed a mathematical relationship that could explain and predict the visible spectrum of hydrogen. Johannes Rydberg – a Swedish physicist – using the work of Balmer developed an equation that related all the wavelengths of lines produced in the electromagnetic spectrum of Hydrogen. The equation is as follows: 1 = (1.097 x 107 m-1) ( 1 – n12 1) n22 Where 1.097 x 107 is the Rydberg constant = RH n1 is the series type n2 is the energy level the electron is transitioning from. Using the Rydberg equation, we can look at the Balmer series and determine the wavelength of visible light emitted by Hydrogen. As mentioned earlier: The hydrogen electron has a variety of transitions from different energy levels. The line spectra that we see is only visible in the visible region of the electromagnetic spectrum. However, there are transitions that occur in ultra violet and infrared region of the spectrum. Series type n1 n1 = 1 n1 = 2 n1 = 3 n1 = 4 Series Name Lyman series Balmer series Paschen series Brackett series Region of spectrum Ultra-violet light Visible spectra of hydrogen Infrared light Infrared light THE BALMER SERIES COLOUR Red Green Blue Indigo Violet n2 3 4 5 6 7 TRANSITION 3 2 4 2 52 62 72 WAVELENGHT 656.2 nm 489.1 nm 434.0 nm 410.1 nm 369.6 nm It is possible to calculate the transitions for other series (Lyman, Paschen, Brackette) using the general Rydberg equation: 1 = RH ( 1 – 2 n1 1) n22 Sample problem: Calculate the frequency and wavelength of transition between n3 and n2 in the Balmer series. n1 = 2 ; n2 = 3 Homework: Calculate the rest of the wavelengths for the light emitted in the Balmer series. Calculate at least one transition in each of the Lyman and Paschen series. Note: Lyman series: any level ground state Paschen series: any level level 3 THE HYDROGEN SPECTRUM ( E = -1311 kJ/mol/n2) -36.4 -52.4 -81.94 -145.67 -327.75 -1311 A continuous spectrum is produced when white light is passed through a prism. The result is line a rainbow, where ROYGBIV can be seen. Absorption Spectra: In order to excite an electron a certain amount of energy is required (at a particular wavelength) corresponding to the differences between the energy levels. For example, an object that absorbs blue, green and yellow light will appear red when viewed under white light. Uses: to identify elements present in a gas or liquid, for example elements in stars and other gaseous objects which cannot be measured directly. Emission Line Spectra: This is the opposite of absorption line spectra. The energy released when an electron falls back down to the ground state (at a particular wavelength) corresponding to the difference between the energy levels. Source: http://www.daviddarling.info/encyclopedia/C/contspec.html NEILS BOHR’ S ATOMIC MODEL There were two main improvements to the historical atomic model. 1. The number of electrons at each principle energy level became known: # electrons = 2n2 where n is the principle energy level evidence/reasoning - ascertained from the intensity of the spectral lines of hydrogen. 2. Electrons must be located in levels of specific and fixed energies (orbits). For the hydrogen the energy at each level can be calculated using the equation given above. Evidence/Reasoning – given that hydrogen gave off four very distinct bands in the spectrum he used Einstein’s and Planck’s work that related first colour to wavelength and then wavelength to Energy, i.e. If the colours were discreet bands of colour the photons must have discreet amounts of energy, since this energy was released when excited electrons dropped from higher energy to lower energy, the electrons must have specific energy levels at which they must exist and not in between. Although Bohr’s model did much to further the understanding of the atom and energies there would be other discoveries that would necessitate change in his model. The wave-particle duality of electron would change the nature of an atom forever… do stay tuned. BOHR MODEL'S LIMITATIONS 1. The electron is a particle whose position and motion can be specified at a given time. 2. An electron moves in an orbit having a fixed radius. 3. Bohr's experimental evidence only agrees with an one-electron atom (Hydrogen) … in addition to this, studies reveal that: Electrons behave as particles in some experiments while in other experiments they behave as WAVES In order to describe the motion of an electron in an atom, both the electron's wave and particle nature must be taken into account. HEISENBERG UNCERTAINTY PRINCIPLE states that due to the dual nature of the electron it is impossible to determine both its position and energy at the same time. ORBITALS Erwin Schrodinger, 1926, used wave equations and calculations that predict the CHANCE of an electron showing up in a particular region of space around the nucleus. This calculated region of space is called an Orbital. Electrons are moving about like bees within the orbital. SOME IMPORTANT DEFINITIONS AUFBAU PRINCIPLE – electrons go into the lowest energy level and fill them in order of increasing energy. PAULI EXCLUSION PRINCIPLE – an orbital can hold a maximum of two electrons. But an orbital can be empty or have one electron. (0,1,2) HUND'S RULE – electrons in the same sublevel or orbitals will not pair up until all the orbitals of the sublevel are at least halffilled. ELECTRONIC CONFIGURATION – distribution of electrons among the various orbitals. Energy Level Diagram n=4 n=3 n=2 n=1 Nucleus