Chapter 7 Quantum Theory of the Atom
Light Waves, Photons and the Bohr Theory
- The Wave Nature of Light
- Quantum Effects and Photons
- Bohr's Model of the Hydrogen Atom
Quantum Mechanics and Quantum Numbers
- Quantum Mechanics
- Quantum Numbers and Atomic Orbitals
Objectives
- describe and relate the wave properties of
Electro-Magnetic Radiation (EMR) using the relationship n =_hc/l
- use Planck's quantum theory E= hn to relate absorbed or
emitted energy to frequency of light.
- describe the significance of Einstein's photoelectric
effect.
- describe the origin of line and continuum spectra.
- list the assumptions made by Bohr in his atomic model .
- explain the concept of an allowed energy state and how
this relates to quantum theory.
- calculate the energy difference between any two allowed
energy states of the electron using Bohr's theory.
- describe the Heisenberg Uncertainty Principle.
- explain the concepts of orbital, and electron density.
- describe the quantum numbers n, l, ml, ms,
and determine their allowed values.
- draw and describe the shapes of the s,p, and d orbitals.
The Wave Nature of Light
Electromagnetic radiation behaves as if it were a wave.
Fundamental terms for wave behavior.
- wavelength- l (meters)
distance between wave crests or troughs.
- frequency- n (1/seconds)
s-1 Hz, number of times a wave crest passes a
specific point.
- velocity- v (m/s), c (m/s)
, how fast the wave front is moving. For EMR,
c = 3.0 * 108 m/s.
- amplitude- A, the height of the wave crest.
- Relationships between terms. Look at UNITS!!
- m * s-1 = m/s
- l * n = c or what's nu?
- Example:
- The orange light from sodium vapor street lights is 589
nm. What is the frequency of this visible radiation?
- Quantum Effects and Photons
- The Nature of EMR- at the end of 19th century (1800's),
it was believed that matter and energy were distinct.
Matter consisted of particles and energy in the form of
waves.
- Planck-1900, Max Planck postulated that energy could only
be absorbed or emitted in whole number packets or quanta
of energy.
Esystem = Ephoton= hn where
h= 6.626•10-34 J•s
Einstein-1905, Albert Einstein proposed that all EMR is
quantized. A stream of particles (energy packets) called photons.
He related mass and energy directly, E=mc2 and using
Planck's result E= nhn, showed that
EMR has a dual nature, acts like a wave, and like a particle.
- E = mc2 = hc / l
==> m= h / cl
- Ephoton = hc/l
Photoelectric Effect
- Electrons are ejected only if the light exceeds a certain
"threshold" frequency.
- Violet light, for example, will cause potassium to eject
electrons, but no amount of red light (which has a
lower frequency) has any effect.
Bohr's Model of the Hydrogen Atom
- Pure gases exhibit line spectra as opposed to continuous
spectra when excited in a discharged lamp.
- Demonstration: incandescent lamp vs discharge lamps
- Bohr's Postulates
- Bohr set down postulates to account for (1) the stability
of the hydrogen atom and (2) the line spectrum of the
atom.
1. Energy level postulate- An electron can have only specific
energy levels in an atom.
2. Transitions between energy levels- An electron in an atom
can change energy levels by undergoing a "transition"
from one energy level to another. (see Figures 7.10 and 7.11)
Bohr proposed an explanation based on quantized transitions
for the electrons.
- Energy is quantized
- En= -RH/n2 ;n=energy
level ; RH= Rydberg's constant
- Ephoton= Ehigher - Elower
= E= hc/l
- A photon is one energy packet - to calculate for a mole
you need to use Avagadro's number.
- The sign of E depends on whether the energy is
given off (-) or absorbed (+)
Examples
1. a. Calculate the energy necessary to move an electron from
n=2 to n= 4 for the hydrogen atom.
b. Is this process exothermic or endothermic?
c. Calculate the wavelength of light emitted or absorbed.
d. What is the color of this wavelength of light?
2. The energy required to dissociate the H2
molecule to H atoms is 432 kJ/mol H2. What is the
wavelength in meters of a photon of light with exactly the energy
dissociate the H2?
Quantum Mechanics and Quantum Numbers
Quantum Mechanics
de Broglie-Louie de Broglie proposed that if EMR can act like
a particle than matter can act like a wave.
- m = h / vl ==> l = h / mv (v since particles can
have any velocity)
- Quantum mechanics is the branch of physics that
mathematically describes the wave properties of
submicroscopic particles.
- We can no longer think of an electron as having a
precise orbit in an atom.
- To describe such an orbit would require knowing
its exact position and velocity.
- In 1927, Werner Heisenberg showed (from quantum
mechanics) that it is impossible to know
both simultaneously.
Heisenberg's uncertainty principle is a relation that states
that the product of the uncertainty in position (x) and the
uncertainty in momentum (mvx) of a particle can
be no larger than h/4p. This only is
significant for very small masses.
Schrödinger Wave Equation- 1926, Erwin Schrödinger proposed
an equation which incorporated the wave and particle nature of
the electron.
Psi is the "wave function". It is function of three
variables: n, l, ml. Y
(n,l,ml) These three variables describe the energy,
and location of the electrons in an atom.
Y (n,l,ml)2
gives the probability of finding an electron in a region of
space. Usually calculated at the 90% probability level. Plots of
this probability density are the "orbitals"
where the electrons are found 90% of the time.
The wave equation is valid or true, only for certain values of
n, l, ml. These are the quantum numbers. These
quantum numbers describe the orbitals (wavefunctions) for the
electrons.
Quantum Numbers and Atomic Orbitals
The Principal Quantum Number, n, (shell)-
- related to the size and energy of the orbital. As
n increases, the orbital gets larger and the electron
spends more time farther away from the nucleus. n =
1,2,3,...º
The Azimuthal Quantum Number, l, (subshell)-
- related to the shape of the orbital. "l"
depends on the value of "n". l = 0, 1, 2,
3,..(n-1), s, p, d, f
The Magnetic Quantum Number, ml, (orbital)-
- relates to the orientation in space of the
orbital. "ml" depends on the value
of "l". ml = -l, ...0,...+l
The Spin Quantum Number, ms, (spin)-
- in a magnetic field, the electron acts as if it is
spinning. It spins either "up" with the field,
or "down" against the field. "ms"
value is either =+1/2 (up) or - 1/2
(down).
Examples:
1. The n quantum number of an atomic orbital is 5.
a. What are the possible values for the azimuthal quantum
number?
b. If l=4, what are the possible values for ml?
2. Which of the following are permissible sets of q.n.s?
| n |
l |
ml |
ms |
| 0 |
0 |
0 |
+1/2 |
| 1 |
1 |
0 |
+1/2 |
| 1 |
0 |
0 |
-1/2 |
| 2 |
1 |
-2 |
+1/2 |
| 2 |
1 |
-1 |
+1/2 |
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Updated Oct.26, 2002. Questions or comments on this Web site
should go to Robin Terjeson.