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Electromagnetic Radiation 1 2 3 c=n.l P How many wavelengths pass through point P in one second? Frequency! 4 Electromagnetic Radiation 5 A radio operator broadcasts at a frequency of 14.2 MHz (megahertz). What is the wavelength of the radio waves put out by the transmitter? c n l 3.0 108 m s 1 3.0 108 m s 1 l 21.1 m 6 1 n 14.2 MHz 14.2 10 s c - Solve example 7.2. - Calculate the wavelengths of the electromagnetic radiation presented in previous slide. 6 Atomic Spectra Now, replace white light source with a hydrogen lamp. 7 cathode H2 → 2H H → H*(excited) H*(excited) → H (Ground state) + light anode أ طاق ة ال و ضع Discharge tube ب 8 Continuous spectrum Line spectrum Problem: No explanation provided by classical physics. Scientists (such as Lyman, Balmer and Paschen) analyzed the observed lines with respect to their wavelengths. Rydberg summarized their efforts in the so-called Rydberg’s equation: R=1.09678×10-2 nm-1 1 1 1 Rydberg’s constant R l n2 1 n22 n: positive integer. 9 Calculate the wavelength, in nanometers, in the line of spectrum of hydrogen Corresponding to n1=2 and to n2=4! 1 1 R 2 2 l n1 n2 1 1 1 1 1 109678 cm 1 2 2 109678 cm 1 l 2 4 4 16 1 3 109678 cm 1 20564.6 cm 1 l 16 1 5 l 4 . 863 10 cm 1 20564.6 cm 1 cm ? nm 1 110 2 m x 10 9 m x 107 1 cm 107 nm l 4.863 10 5 cm 4.863 10 5 107 nm 486.3 nm Green light 10 Energy of Light - Energy of electromagnetic waves -However, Planck (Black body radiation) Einstein (photoelectric effect) hn hn hn hn hn hn hn hn hn hn Light composed of tiny particles, called quanta (photons) Energy of each photon (quantum) = h × n Number of photons determines light intensity. Ephoton = h × n h=6.6×10-34 J.s Planck’s constant 11 Bohr’s Theory Bohr’s Postulates: •Electron moves in circular orbits around the nucleus. •Electron can possess only certain energy values corresponding to the orbit. •Electron can “jump” from one orbit to another, the energy difference will be emitted or absorbed in the form of light quanta. 12 1 En A Z 2 n 2 A=2.18×10-18 J=13.6 eV Z : atomic number n : positive integer = 1, 2, 3, … 13 The larger n - the larger is the orbit size, the farther is the electron from nucleus - the larger is the electron energy Comparison to throwing stone upwards. Negative sign means that the electron is under the influence of the nucleus. Electron free from nucleus attracting force when n=∞. 14 Explanation of line spectrum A E Ehigh Elow 2 2 nhigh nlow A 1 1 E A 2 2 h n n low nhigh A 1 1 n 2 2 h nlow nhigh c n l nhigh nlow A 1 1 2 2 l c h c nlow nhigh 1 n A R hc 15 Lyman series ends at n=1 UV Balmer Series ends at n=2 visible Paschen Series ends at n=3 Infra-red 16 Example 7.5 Calculate the energy, frequency and wavelength of the photon emitted when an electron in the hydrogen atom drops from the fifth to the second energy level. 1 1 E photon E A 2 2 n n low high 1 1 E photon 2.18 10 18 2 2 J 4.578 10 19 J 2 5 E photon 4.578 10 19 J 14 1 n 6 . 94 10 s 34 h 6.6 10 J s 3.0 108 m s 1 7 l 4 . 325 10 m 432.5 nm 14 1 n 6.94 10 s c 17 De Broglie Hypothesis Light behaves: - as waves (electromagnetic waves) Hertz experiment - as particles (photons) Photoelectric effect, Compton effect Why should light be special??!!!!! De Broglie suggested: Generalization of dual nature (wave nature & particle nature) to all matter. Any moving object can be considered to be a wave!!! Energy of that object is E=mc2 If object considered to be a wave, E=hn 18 h n m c 2 h c l h m c2 h l mc l mc h l mv h l p De Broglie relation De Broglie wavelength Experimental evidence: electron diffraction Diffraction is a phenomenon that only waves can undergo Includes waves interference 19 Example: Calculate the wavelength of a football player weighing 60 kg moving in the yard with 10 km/h velocity. v 10 km / h 10000 m 2.778 m / s 3600 s h 6.6 10 34 Js s l 3.96 10 35 m m v 60 2.778 kg m too small to be observed experimentally Example: Calculate the wavelength of an electron moving with a velocity of 1000 km/h. h 6.6 1034 J s s 10 l 7 . 25 10 m 7.25 Angstrom 31 m v (9.1110 ) 1000000 kg m X-ray: diffraction on crystals 20 Wave mechanics A version of quantum mechanics (modern concepts in physics) Electron in atoms are considered to be standing waves. Each electron in atom is described by a set of numbers called Quantum numbers. 21