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Unformatted text preview: Worksheet 1O  Electromagnetic Radiation and the Bohr Atom Light is known to have the wavelike 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 6fNX/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”’”fi‘ / .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‘fydrxwM’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 14] 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‘4rr' “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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 Spring '11
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