waves & bohr’s theory chapter 7 §1-4. waves wavelength, λ, in meters (m) the length of a...
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Waves &
Bohr’s TheoryChapter 7 §1-4
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Waves
Wavelength, λ, in meters (m)The length of a wave from crest to crest or trough to
trough.
Frequency, υ, in inverse seconds (s-1)The number of waves that pass in a given amount
of time.
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Light’s Wave Characteristics
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Light’s Wave Characteristics
Speed of light equation
c c = speed of light, 3.00x108 m/sλ = wavelength, in mν = frequency, in Hz or s–1
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Light’s Wave Characteristics
What is the frequency of red light having a wavelength of 681 nm?681 nm = 6.81x10–7 m3.0x108 m/s = (6.81x10–7 m)(υ)υ = 4.41x1014 s–1
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Max Planck
Quantized
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Planck’s Equation
n = integer other than zero, no unit, represents the energy level of the atomh = Planck’s constant, 6.63x10–34 J•sν = frequency, in Hz or s–1
E = energy of a quantum – amount of energy to move an e– from its present energy to its next higher one
E nh
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The Photoelectric Effect
Although the photoelectric effect was first discovered by Heinrich Hertz in 1887, Albert Einstein incorporated Planck’s ideas into the explanation of the photoelectric effect.
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The Photoelectric Effect
Einstein stated that electrons could move within their atoms if a minimum amount of energy were reached.
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Let’s Practice
The blue-green line of the hydrogen atom spectrum has a wavelength of 486 nm. What is the energy of a photon of this light? 486 nm = 4.86x10–7 m
3.0x108 m/s = (4.86x10–7 m) (υ)υ = 6.17x1014 s–1
E = (1)(6.63x10–34 J•s)(6.17x1014 s–1)E = 4.09x10–19 J
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Bohr’s Line Spectra
Bohr noticed that elements emitted a line spectrum.
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Bohr’s Line Spectra
He hypothesized that each line in the spectra were created when an electron fell from a higher energy level to a lower one within the atom.
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Bohr’s Line Spectra
Here, the electron of the hydrogen atom is shown moving between the various energy levels.
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Bohr’s Postulates
Bohr felt the need to explain two main issues: 1st – If electrons are negative
and protons are positive…..
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Bohr’s Postulates
Bohr felt the need to explain two main issues: 2nd – How are the line spectra
being created?
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Bohr’s Postulates
Postulate #1:Electrons only have specific
energy values and energy levels.
= the energy of a particular e– energy level
= the Rydberg constant = 2.18x10–18 J = integral value representing the
energy level (principal quantum number
2HREn
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Bohr’s Postulates
Postulate #2:Electrons become excited by
collisions of atoms or absorption of energy – think of anything colored… it absorbs light to later emit (reflect) other colors
Electrons can change energy only by going from one energy level to another – making a transition.
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Bohr’s Postulates
Postulate #2:The electron
absorbing energy
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Bohr’s Postulates
Postulate #2:When an electron falls from a
higher energy level to a lower energy level, it emits a photon of light.
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Bohr’s Postulates
Postulate #2: This energy of this photon
can be found by:
2 2f i
H Hn n
f i
R RE E E
n n
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Bohr’s Postulates
Postulate #2: Remember that the energy of
a photon can be determined by:
2 2f i
H Hn n
f i
R RE E E
n n h
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Bohr’s Postulates
Postulate #2: Which can be related to
wavelength:
2 2f i
H Hn n
f i
R RE E E
n n h
ch
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Bohr’s Postulates
Postulate #2:Which leads to the Balmer
equation:
This equation can calculate the wavelength of any electron falling to the 2nd energy level – emitting visible light.
7 12 2
1 1 11.097 10
2 i
x mn
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Bohr’s Postulates
Postulate #2:By the end of Experiment
#13, you should be able to identify the Balmer Series, along with the Paschen Series and the Lyman Series.
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Let’s Practice
What is the wavelength of the light emitted when the electron in a hydrogen atom undergoes a transition from energy level n = 6 to level n = 3?
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Let’s Practice
What is the wavelength of the light emitted when the electron in a hydrogen atom undergoes a transition from energy level n = 6 to level n = 3?
∆E = E3 – E6 =
υ = 2.74x1014 s–1
c = λυ → 3.0x108 m/s = λ (2.74x1014 s–1)
λ = 1.09x10–6 m = 1090 nm (Infrared)
18 1819
2 2
2.18 10 2.18 101.82 10
3 6
J Jx J
19 341.82 10 6.636 10x J x J s