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Lecture September 19
Goal for today: finish Chapter 7
(almost) Sec. 7.6 with Chap.8
Packet of light is also a “particle”
called a photon
Energy of a
photon of
light
E = hν
OR
E = hc/λ
h = 6.626 x 10-34 J-s
Planck’s constant
CHEM131 - Fall 11 - September 19
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The Hydrogen Atom and the
Bohr Model
1H
atom is a proton
surrounded by an electron
n=1
An over simplified
model but very
instructive
Three
distinct
orbits
n=2
n=3
Quantized
CHEM131 - Fall 11 - September 19
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Rydberg Formula
n=2
En = -Rhc/n2
Rhc = 2.179 x 10-18 J/atom
E2 = -[(2.18 x 10-18)/22] J/atom
=-0.545 x 10-18 J/atom
ΔE = Efinal - Einitial =
(-2.18 x 10-18) - (-0.545 x 10-18)
=-1.64 x 10-18 J/atom ✮energy emitted
- photons
n=1
E1 = -2.18 x 10-18 J/atom
See Fig. 7.21
CHEM131 - Fall 11 - September 19
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Energy
Wavelength
h = 6.626 x 10
J-s
E = hν = hc/λ
c =2.998 x 10 m/s
OR λ = hc/E
-34
8
What wavelength of light is ΔE = 1.63 x 10-18 J/atom?
(n=2 ➞ n=1)
λ = (6.626 x 10-34 J●s)(2.998x108 m/s)/(1.63 x 10-18 J/atom
=1.22 x 10-7 m OR 122 nm (Fig 7.12)
Not visible - ultraviolet (uv) region
Comment: the per atom is the same as a single photon.
E/mol = 1.63 x 10-18 J/atom x
(6.022 x 1023 atoms/mol) = 982 kJ/mol
CHEM131 - Fall 11 - September 19
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Emission and Absorption Spectra
ΔE = -Rhc (1/nf2 - 1/ni2)
ΔE negative =
emission
ΔE positive =
absorption
nf = ∞
n1 =2
Balmer - visible
ionize the atom complete removal of
the electron
CHEM131 - Fall 11 - September 19
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Electromagnetic
Spectrum See Fig. 7.5
CHEM131 - Fall 11 - September 19
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Example
What wavelength of light is needed to
completely ionize hydrogen that is initially
excited to the n=3 energy level?
ΔE = -Rhc [(1/∞) - 1/32)] = -2.179 x 10-18(-1/9)
= 2.421 x 10-19 J
Absorption positive!!
ΔE = E photon = hν = hc/λ
λ = [(6.626 x 10-34 J-s)(2.998 x108 m/s)]/
(2.421 x 10-19 J)
Wavelength cannot
Ans: 820.5 nm
be negative!!
CHEM131 - Fall 11 - September 19
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Introduction to Quantum
Mechanics
Two important scientific advances that
shaped the way we view electronic
structure
Particles (electrons) can have wave-like
properties
de Broglie wavelength λ = h/mv
Electron E(n=1) = 2.18 x 10-18 J ☞
λ = 330 pm
me=
9.11x10-31kg
Size of a Bohr n=1 radius = 53 pm
CHEM131 - Fall 11 - September 19
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More on Quantum Mechanics
AND
Uncertainty Principle - cannot know both
the energy (momentum) and the position
of a particle - an electron
Talk about it in terms of probability and
WAVE FUNCTIONS
Schrodinger Equation HΨ = EΨ
Ψ is called the wave function that describes
the spatial of the electron in the atom
CHEM131 - Fall 11 - September 19
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Quiz of the Day
What is the energy of the photon that is
absorbed when the hydrogen atom initially
in its ground state (n=1) is excited to the
n=5 state?
ΔE = -Rhc [(1/52) - 1/12)] =
-2.179 x 10-18(0.04-1) = 2.092 x 10-18 J
CHEM131 - Fall 11 - September 19
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