Download Quantum Model of an Atom

Quantum Model of an Atom
• 7.1, 2: Intro, Energy and Light
• 7.3: The Bohr Model and Spectroscopy
• 7.5, 6: The Organization of the Atom
– Orbitals!
We will completely omit topics in section 7.4
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Electromagnetic Radiation
Electromagnetic radiation is a combination of
oscillating electric and magnetic fields
Wavelength (λ) = Distance between two successive peaks.
Frequency (ν) = Number of peaks observed in a given interval of time.
The two are related with the speed of light = c = 2.99 x 108 m/s = λν
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Electromagnetic Spectrum
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Wave-Particle Duality
The study of blackbody radiation (Planck, 1903) and the
photoelectric effect (Einstein, 1905) led to the
“realization” that light energy, and therefore electrons,
behaved as both a wave and a particle, called a photon.
• Dr. Quantum and the “Double Slit” Experiment
Energy is quantized!!!
E = hν
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h = Planck’s constant
= 6.626 x 10-34 J•s
ν = Frequency (Hz, or s-1)
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Energy-Light Relationships
We typically relate light in terms of wavelength,
not frequency!
Write the energy relationship in terms of wavelength
instead of frequency:
Is the relationship between energy and frequency direct
or inverse?
Is the relationship between energy and wavelength
direct or inverse?
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Energy-Light Relationships
What is the frequency of light emitted from a photon with an energy
of 2.15 x 10-23 J?
What is the energy of a photon with a wavelength of 350 nm, in J?
In kJ/mol?
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The Bohr Model (1913)
Electrons lie in discrete,
circular “orbitals” around
a nucleus.
Developed for atoms
containing 1 electron.
Bohr’s Postulates:
1. Energy level: An e- can only have specific energy values in an
atom.
2. Transitions: An electron can change energy by traveling from
one energy level to another.
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The Bohr Model
En = -
Z
n
Z=
2
2
Rh
n = Energy level
Rh = Rydberg Constant = 2.18 x 10-18 J
This can be used for any one-electron system, such as H, C+5, Fe+25…
Determine the energy, in kJ, for an n = 3 electron in Hydrogen. What
wavelength of light does this energy correspond to?
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The Bohr Model
How do we calculate the energy associated with a transition?
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The Bohr Model
Calculate the energy required to promote an electron from the n=2
level to the n=4 level in hydrogen.
What wavelength of light is omitted when an electron in hydrogen
relaxes from n=6 to n=3?
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Quantum Numbers
The Schrödinger Wave Equation
ψ(n, l, ml) ← the wave function that describes the energy and
locations of an electron in any atom.
n = Principal quantum number = 1, 2, 3…
l = Angular momentum q.n. = 0, 1,…, (n-1)
ml = Magnetic q.n. = (-l,…,0,…,+l)
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Organization of Quantum Numbers
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The Orbitals!
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The Orbitals!
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The Orbitals!
For a cool representation of the orbitals: www.orbitals.com/orb/orbtable.htm
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