Download Chapter 32 Quantum Picture of Atoms Lecture 37

Lecture 37
Chapter 32
Quantum Picture of Atoms
Quiz 5: Monday Dec. 6 (Chaps. 29-32)
29-Nov-10
© 2010 Pearson Education, Inc.
ATOMIC STRUCTURE
Present Concepts - An atom is an electrically neutral
entity consisting of negatively charged electrons (e-)
situated outside of a dense, positively charged nucleus
consisting of positively charged protons (p+) and
neutral neutrons (n0).
Z (atomic number) = # of electrons = # of protons
A (mass number) = # protons + # neutrons
Particle
Charge
Electron
-e
Proton
+e
Neutron
0
19
e = 1.6 x 10 C
© 2010 Pearson Education, Inc.
Mass
9.109 x 10 -31 kg
1.673 x 10 -27 kg
1.675 x 10 -27 kg
ATOMIC STRUCTURE
Nucleus
Model of a
Helium-4
(4He) atom
Z=2
A=4
e-
p+no
no p+
eElectron Cloud
How did we get this concept? - This portion of our
program is brought to you by:
Democritus, Dalton, Thompson, Planck, Einstein, Millikan,
Rutherford, Bohr, de Broglie, Heisenberg, Schrödinger,
Chadwick, and many others.
© 2010 Pearson Education, Inc.
Discovery of the Electron
• Electrodes in a cathode-ray
tube under low pressure are
connected to a voltage
source, causing the gas to
glow due to a “ray”
emerging from the negative
terminal (the cathode).
• Slits could make the ray
narrow and plates could
prevent the ray from
reaching the positive
terminal (the anode).
© 2010 Pearson Education, Inc.
Discovery of the Electron
• When electric charges
were brought near the
tube, the ray bent toward
positive charges and
away from negative
charges.
• The ray was also
deflected by the
presence of a magnet.
• These findings indicated
that the ray consisted of
negatively charged
particles.
© 2010 Pearson Education, Inc.
Discovery of the Electron
Thomson reasoned that the amount of the
beams’ deflection depended on the mass of
the particles and their electrical charge.
• The greater each particle’s mass, the greater
the inertia and the less the deflection.
• The greater each particle’s charge, the greater
the force and the greater the deflection.
• The greater the speed, the less the deflection.
• Thomson determined the charge/mass ratio of
electrons
© 2010 Pearson Education, Inc.
Measurement of Electron Charge
• Millikan sprayed tiny oil droplets into a chamber
between electrically charged plates—into an electric
field.
• He adjusted the field so that droplets hovered
motionless, i.e., when downward force of gravity was
balanced by upward electrical force.
• He found that the charge
on each drop was always
some multiple of a single
value – the charge of
each electron.
© 2010 Pearson Education, Inc.
ATOMIC STRUCTURE
R. A. Millikan - Measured the charge of the electron.
In his famous “oil“oil-drop” experiment, Millikan was able to
determine the charge on the electron independently of its
mass. Then using Thompson’s chargecharge-toto-mass ratio, he
was able to calculate the mass of the electron.
e = 1.602 10 x 10-19 coulomb
e/m = 1.7588 x 108 coulomb/gram
m = 9.1091 x 10-31 kg
Goldstein - Conducted “positive” ray experiments that
lead to the identification of the proton. The charge
was found to be identical to that of the electron and
the mass was found to be 1.6726 x 10-27 kg.
© 2010 Pearson Education, Inc.
“Plum Pudding” Model of Atom
( from About 1900)
© 2010 Pearson Education, Inc.
Discovery of the Atomic Nucleus
In Rutherford’s experiment, a beam of positively charged
alpha particles (2P+2N) was directed onto a thin gold foil.
•
•
•
•
Nearly all alpha particles passed through with little or no deflection.
Some particles were deflected from their straight-line paths.
A few alpha particles were widely deflected, and
A very small number were even scattered backward!
© 2010 Pearson Education, Inc.
Alpha Particle Deflections in Plum
Pudding Model vs. Nucleus Theories
© 2010 Pearson Education, Inc.
ATOMIC STRUCTURE
If the plum pudding model is correct, then all of
the massive α-particles should pass right through
without being significantly deflected.
In fact, most of the α - particles DID pass right
through. However, a few of them were deflected at
high angles, disproving the “plum pudding” model.
© 2010 Pearson Education, Inc.
“It was almost as incredible as if
you fired a 15-inch shell at a piece
of tissue paper, and it came back
to hit you!”
--E. Rutherford
(on the ‘discovery’
of the nucleus)
Discovery of the Atomic Nucleus
These alpha particles must have hit something
relatively massive—but what?
• Rutherford reasoned that the undeflected particles
traveled through empty space in regions of the
gold foil, while the small number of deflected
particles were repelled from extremely dense,
positively charged central cores.
• Each atom, he concluded, must contain one of
these cores, which he named the atomic
nucleus.
• The very dense nucleus contains all of the atom’s
positive charge and most of the mass, and is
surrounded by electrons that “orbit” around the
nucleus, much as the planets orbit around the sun.
© 2010 Pearson Education, Inc.
Nuclear Model of the Atom
• What “orbits” can electrons in an atom occupy,
and what is the shape of the orbits?
• We know from our
study of light emitted
from excited atoms
that there are certain
allowed energies for
orbiting electrons.
• The frequencies
(energies) of light in
the spectrum of a
particular atom
provide clues.
© 2010 Pearson Education, Inc.
Atomic Spectra: Clues to Atomic Structure
• An important sequence of lines in the hydrogen
spectrum starts with a line in the red region, followed by
one in the blue, then by several lines in the violet, and
many in the ultraviolet.
• Spacing in frequency between successive lines
becomes smaller and smaller from the first in the red to
the last in the ultraviolet, until the lines become so close
that they seem to merge.
© 2010 Pearson Education, Inc.
Frequency
Atomic Spectra: Clues to Atomic Structure
• Balmer first expressed the wavelengths of
these lines in a single mathematical
formula.
– He was unable to provide a reason why his
formula worked so successfully.
• Rydberg noticed that the frequencies of
lines in certain series in other elements
followed a formula that the sum of the
frequencies of two lines in such series often
equals the frequency of a third line.
© 2010 Pearson Education, Inc.
Bohr’s Model of the Atom
• Bohr reasoned that electrons occupy
“stationary” states (of fixed energy,
not fixed position) at different
distances from the nucleus.
• Electrons can make “quantum
jumps” from one energy state to
another.
• Light is emitted when such a
quantum jump occurs (from a higher
to a lower energy state).
• Frequency of emitted radiation is
determined by
∆E = hf
where ∆E is the difference in the
atom’s energy when the electron is
in the different orbits.
© 2010 Pearson Education, Inc.
Questions about Bohr’s Model
• Why are only certain orbits allowed, and
what determines the allowed energies?
• According to classical theory, an electron
in orbit is accelerating and should
continuously emit radiation, thus losing
energy.
• This loss of energy should cause the
electron to spiral rapidly into the nucleus,
but this does not happen.
© 2010 Pearson Education, Inc.
Explanation of Quantized Energy
Levels: Electron Waves
• Louis de Broglie hypothesized that a wave
is associated with every particle (as we
saw last lecture).
– The wavelength of a matter wave is inversely
related to a particle’s momentum. λ = h/p
• de Broglie showed that a Bohr orbit exists
where an electron wave closes on itself
constructively.
– The electron wave becomes a standing wave,
like a resonant wave on the string of a guitar.
© 2010 Pearson Education, Inc.
Explanation of Quantized Energy
Levels: Electron Waves
In this view, the electron is thought of not as a particle located
at some point in the atom but as if its mass and charge were
spread out into a standing wave surrounding the atomic
nucleus with an integral number of wavelengths fitting evenly
into the circumferences of the orbits, as in (a) below.
© 2010 Pearson Education, Inc.
Explanation of Quantized Energy
Levels: Electron Waves
(a) An orbiting electron forms a standing wave only when the
circumference of its orbit is equal to a whole-number
multiple of the wavelength, as in (a) below.
(b) When the wave does not close in on itself in phase, it
undergoes destructive interference (as in (b)). Hence, orbits
exist only where waves close in on themselves in phase.
© 2010 Pearson Education, Inc.
Explanation of Quantized Energy
Levels: Electron Waves
The circumference of the innermost orbit,
according to this picture, is equal to one
wavelength.
• The second has a circumference of two
electron wavelengths.
• The third orbit has a circumference of three
electron wavelengths, and so forth.
© 2010 Pearson Education, Inc.
Explanation of Quantized Energy
Levels: Electron Waves
• The electron orbits in an atom have discrete radii
because the circumferences of the orbits are wholenumber multiples of the electron wavelength.
• This results in a discrete energy state for each orbit.
© 2010 Pearson Education, Inc.
Explanation of Quantized Energy
Levels: Electron Waves
• This model explains why electrons don’t spiral
closer and closer to the nucleus, causing atoms to
shrink to the size of the tiny nucleus.
• If each electron orbit is described by a standing
wave, the circumference of the smallest orbit can
be no smaller than one wavelength.
– No fraction of a wavelength is possible in a circular (or
elliptical) standing wave.
• As long as an electron forms a “resonant” standing
wave with an allowed energy, it will be stable and
will not lose energy unless it moves to a new orbit.
© 2010 Pearson Education, Inc.
Quantum Mechanics
The details of the shape of the electron orbits are
given by the theory of Quantum Mechanics
• Quantum mechanics describes all particles as
matter waves, with a “wave function” whose
amplitude is related to the probability of finding
the particle in a certain region.
• Schrödinger’s wave equation replaces
Newton’s laws for finding where a particle is
likely to be and how it is likely to move.
© 2010 Pearson Education, Inc.
Probability Density of Electron in
Hydrogen Atom Orbits
The density of dots plotted below is proportional to
electron probability density for different “orbits”.
First two orbits
First orbit
Quantum Mechanics
CHECK YOURSELF
As to why electrons orbit in only certain orbits, a compelling
explanation views orbital electrons as
A.
B.
C.
D.
particles that morph into waves.
standing waves.
planetary particles.
quantum particles.
© 2010 Pearson Education, Inc.
Quantum Mechanics
CHECK YOUR ANSWER
As to why electrons orbit in only certain orbits, a compelling
explanation views orbital electrons as
A.
B.
C.
D.
particles that morph into waves.
standing waves.
planetary particles.
quantum particles.
Explanation:
Standing waves are stable and close in on themselves
in phase. Only certain standing waves frequencies are
possible.
© 2010 Pearson Education, Inc.
Correspondence Principle
Correspondence principle
• The correspondence principle, first stated by
Niels Bohr is:
– If a new theory is valid, it must account for the verified
results of the old theory.
• New theory and old must correspond; that is, they must
overlap and agree in the region where the results of the old
theory have been fully verified.
• Quantum mechanics and Newton’s laws must
agree when dealing with objects much larger
than atoms.
© 2010 Pearson Education, Inc.
Correspondence Principle
CHECK YOURSELF
To which of these does the correspondence principle
apply?
A.
B.
C.
D.
The Schrödinger equation leads to Newton’s equations
for orbital motion of satellites.
The kinetic energy of a 1-kg mass moving at 1 m/s can
be found from Newton’s Laws or Schrodinger’s equation
Diffraction can be explained with either waves or
photons.
All of the above.
© 2010 Pearson Education, Inc.
Correspondence Principle
CHECK YOUR ANSWER
To which of these does the correspondence principle
apply?
A. The Schrödinger equation leads to Newton’s equations
for orbital motion of satellites.
B. The kinetic energy of a 1-kg mass moving at 1 m/s can
be found from Newton’s Laws or Schrodinger’s equation
C. Diffraction can be explained with either waves or
photons.
D. All of the above.
Explanation:
Unlike Heisenberg’s uncertainty principle, the
correspondence principle is a general rule. Old
and new theory must overlap where both are
valid.
© 2010 Pearson Education, Inc.
Key Points of Lecture 37
• Discovery of the Atomic Nucleus
• Discovery of the Electron
• Atomic Spectra: Clues to Atomic Structure
• Bohr’s Model of the Atom
• Explanation of Quantized Energy Levels: Electron Waves
• Quantum Mechanics
• Correspondence Principle
z Before Friday Dec. 3, read Hewitt Chap. 31.
z Homework #25 due by 11:00 PM Friday Dec. 3
z Homework #26 due by 11:00 PM Sunday Dec. 5
© 2010 Pearson Education, Inc.