Worksheet 10 answers

Worksheet 10 answers - Worksheet 1O - Electromagnetic...

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Unformatted text preview: Worksheet 1O - Electromagnetic Radiation and the Bohr Atom Light is known to have the wave-like properties of frequency (u) and wavelength (A). These are iilustrated below. The x—axis is a measure of time. The distance between the peaks is called the wavelength and the number of waves per unit time (1 second in this example) is called the number of cycles. The first wave pattern has 2 cycles per second, the middie example has 4 cycles per second and the example on the right has 8 cycles per second. This is the frequency of the wave, and has the units of hertz. Hz (cycles/s). fim—fl H H —____......__—._..._..m.._.____.__ 1 second As the frequency increases, the wavelength decreases. In Electromagnetic radiation (light) these are related by the equation: 0 = A1) where c = the speed of light. 2.998 x 108 mls, 9... = wavelength (m) and u = frequency (s’1 or Hz). The electromagnetic spectrum (EMS) is shown below. Which color of visible light has the shortest waveiength? Which radiation has wavelengths longer than visible light? H M: I, ,2, 4—~_——.__.___._._....___ Increasing energy ——-————-—-—-—-—-—-——- M increasing wavelength -—-—----——————+— 0.000] nm 0.01nm iOnm 1000 mm 0.01 cm icm 1m 100m Gamma rays infrared Radio waves Radar TV FM AM Visible lig hi 400 nm 500 nm 600 nrn 700 nm 1. The wavelength of green light is about 522 nm. What is the frequency of this radiation? 6 :lfl 2.99?x/0'@,zt- f22x19'9m 5' 1h iH/r/a”$" 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 is. t? 7 22/02: 10" Hz: (5") 9”?" r k C: A? ngfxyoi/figz ZJC’K/ ,. f). A: r $43 axed/try /¢2;flm Planck recognized that energy is quantized and reiated the energy of radiation [1 ,q’ (emitted or absorbed) to its frequency. AE=nhv a MM ‘1‘ where n = integer and h = Planck‘s constant = 6.626 x 103‘4 J s 3. Which of the following are directly related? 3) energy and wavelength * M) If??? {(-53 Mad?" b) wavelength and frequency - mm 4056!" 0) frequency and energy , MCI/5 , 927/” 4. A classical radio station broadcasts at 93.5 MHz (M r: 105). Find the wavelength of this radiation, in meters, and the energy of one of these . . . . . ,P S photons, In J. What type of radiation IS this. C 7 fit? Z 3”] mfg? : 935%,0541A 95s'xm‘l/z =7) E 45’5279 6-fNX/o'”?:rv?5.5‘xm‘ argwm ’4 6 f {.10 r/a’Z‘J” flm’owam 5. What is the energy of a photon with: ( FM) a) a wavelength of 827 nm? What type of radiation is it? E 1 Am : ,er ., 5,6221): 10'3‘03- Zn ifs/’0’”?! a 0 x/d '9 T w hm 2,4“ A 522? 4/0"?»7 "— iz?nm= mar/#2 b) a wavelength of 1 nm? What type of radiation is it? w £67 [16 : 5'.(2€Xfa'!(jf "2‘9966zx/afflifljgm T [IN/X/O'J‘T . Xn’rfldn‘? X \L ' Y Bohr applied this concept to the 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 an atom. Electrons are allowed to move between these energy levels. The light emitted by the elements is a measure of the energy gap between the two electronic states. For the hydrogen atom, AE = R“ z2 1 - 1 RH z Rydberg constant = 2.178 x 104% E 2 “i Z = nuclear charge 2 1 for H, 2 for He 6. Calculate the AE for the n = 4 to the n = 2 transition in hydrogen. Where on the EMS would this appear? What does the sign mean? .i.E'=—72.rrrx;o”’”f-i‘ / .L) 2! p 4 I 46" — 4,0gX/a"’j d E : fa. <2 . 4,1153% /0""«?fy gas/a “M3;- zea; “Mm/I ,A , r5 4 — raid AW 1’7 e 45': x317; r 145%; fix/6%... 7. 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 = ?). W I M . A6 {ac r "WM " t“ m" T..—:i?’"f. T'L‘I’i MN Mix x {6"} n; flak.» f x. “If- -. , 7 “ mitt” erym - yg‘fydrxw-M’jn/z 1/1 _ I] L r r” Wm? it” 2%» as; W” Ionization energy is the energy required to completely remove an electron from and atom. This can be thought of as the transition between n r: 1 and n = 00. 8. Calculate the energy needed to remove the electron from hydrogen in its ground state. $6" w9,/}al"2rr’o"“'"I“! a 1-4] in T 0 90" g A { :i.~(j./?'fk fi’MJ /) A 6 r i/lH’x/O’WJ Wold/QM We}: MAW/Ha This is the energy to remove an electron from the ground state of hydrogen. What wavelength of light would work? Where is this on the EMS? ‘ - Z r r “I g (2w.ro"5‘4r--r' “5’” 155* if r . - . . ~7- . . t; 2% ” a; t QIEKJQ’F I}? 9]; r“ a e I. «__, I33)” M V 9. What is the energy needed to remove the remaining electron from He+ in its ground state? Is it easier or harder to remove the electron from He+ than from H? - g - m. w 3 I __ fig“ It; 0 as? 2 v =' flit/2 xxo””f ...
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This note was uploaded on 12/05/2011 for the course CHEM 231 taught by Professor Beck during the Spring '11 term at Indiana.

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Worksheet 10 answers - Worksheet 1O - Electromagnetic...

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