Quanta to Quarks
Focus Area 1
This is how some
feel….but we won’t!
Light (Again)
Isaac Newton first showed that white light was made up of
all the colours of the visible light spectrum by shining a ray
of white light through a glass prism.
In 1801 William Wollaston repeated the experiment using
sunlight and found that there were narrow dark bands in the
solar spectrum.
These were investigated
further by Fraunhofer using
his new invention, the
spectroscope, in 1814.
Fraunhofer found 574 dark
lines, which became known as
Fraunhofer lines.
Spectral lines were studied
further throughout the
nineteenth century, most
significantly by Gustav
Kirchhoff who formulated the
three laws of spectroscopy.
Kirchhoff’s laws describe the three situations by which
spectra are produced and the spectra that are produced by
them. They are:
1. A hot solid body (or a hot dense gas) produces a
continuous spectrum. This is the spectrum first
described by Newton and can be seen in a rainbow.
2. A hot gas under low pressure produces an emission
spectrum. An emission spectrum appears as a
number of distinct narrow lines on a black
background.
3. A cool gas under low pressure produces an
absorption spectrum when a continuous spectrum of
light passes through it. An absorption spectrum
appears as a continuous spectrum interrupted by
narrow dark lines. Wollaston and Fraunhofer
observed an absorption spectrum when they
examined the spectrum of sunlight.
We need to
remember
that by the
end of the
1800s,
people still
had no
idea what
caused
these
spectral
lines.
EXP: Hydrogen Spectra
History of the atom (Brightstorm video)
http://youtu.be/gT6nsloIRa8
Thomson’s Atomic Model
With the discovery if the
electron in 1897, Thompson
proposed a model of the atom
known as the 'plum pudding
model'.
In this model, the atom was
composed of electrons (which
Thomson still called
corpuscles), surrounded by a
soup of positive charge to
balance the electrons'
negative charges, like
negatively-charged "plums"
surrounded by positivelycharged "pudding".
The next big thing
The next major advance in our
understanding of the atom came
in 1909, as a result of an
experiment conducted by Hans
Geiger and Ernest Marsden.
Geiger and Marsden were
students of Ernest Rutherford,
who himself had been a student
of Thomson’s.
Geiger and Marsden used alpha
particles to examine the
distribution of charge in an
atom.
They used a thin piece of gold foil as their target, which
they surrounded by a circular sheet of zinc sulfide.
The alpha particles illuminated the zinc sulfide when
they struck it.
This allowed Geiger and Marsden to measure the
deflection of the alpha particles by the atoms in the
gold foil.
PhET:
Rutherford
scattering jar
Geiger and Marsden expected that any
deflection detected would be small as
the positive charge was distributed
evenly throughout the atom in
Thomson’s model.
However, their actual results were
most unexpected. They found that
most alpha particles were not
deflected at all, but of those that were
deflected, some were deflected by
much more than 90°, and some were
even deflected 180°.
Rutherford realized that this result
could not have been produced if
positive charge in an atom was diffuse.
Therefore, the positive charge in an
atom must be concentrated in a
volume much smaller than the whole
atom. (He first used the word ‘nucleus’
in 1912).
Rutherford’s Atom
http://youtu.be/FfY4R5mkMY8
A new model
Rutherford used the results of
the gold foil experiment to
develop his own model of the
atom.
The Rutherford model consisted
of a massive, positively charged
nucleus surrounded by a cloud of
negatively charged electrons.
The vast majority of the volume
of Rutherford’s atom was empty
space.
Rutherford’s model fitted the
experimental data of both
Thomson’s experiment and the
Geiger-Marsden experiment.
The Rutherford model was a great step
forward in our understanding of atomic
structure but it still had its limitations.
To overcome for force of attraction
between the positive nucleus and the
electrons, electrons must be in circular
motion (much like the planets around the
Sun).
Since electrons were in circular motion,
they would be experiencing acceleration
and accelerating charges were known to
emit electromagnetic radiation.
This loss of energy would cause the
electrons to spiral closer to the nucleus
(like orbital decay for satellites) and
matter would be destroyed.
This was clearly not happening so there
were problems with the model.
Back to Hydrogen
When hydrogen gas is excited by a large potential
difference, it produces the characteristic emission and
absorption spectra.
A series of spectral lines that were found in the visible light
section of the electromagnetic spectrum were called the
Balmer series.
Spectral lines were also found to exist in other sections of
the EM spectrum and these were given other names.
Rutherford's model could not explain spectral lines
either.
As electrons spiralled toward the nucleus with
increasing speed, they should emit radiation of all
frequencies, not just the one frequency
corresponding to the wavelength of the spectral line.
Thus, the observed spectrum of the element should
have been continuous and not a line spectrum.
Now what?
By the turn of the 20th Century physicists understood the
conditions by which hydrogen’s spectral lines were
produced and the mathematical relationship that
determined the wavelength of the spectral lines.
In 1885 Johann Balmer published a mathematical equation
that correctly predicted the wavelength of the lines in the
hydrogen spectra:
where h = 3.6456 × 10-7 m, and m is an integer greater than
2. Substituting m = 3, 4, 5, and 6, Balmer was able to
calculate the wavelength of hydrogen’s spectral lines.
Balmer did not propose an explanation
of why spectral lines were produced. He
simply examined the data and found a
mathematical relationship that described
it.
Three years later Johannes Rydberg
modified Balmer’s equation. Rydberg’s
equation was:
where R = 1.097 × 107 m, and n1 and n2 are
both integers with n1<n2 . Balmer’s
equation is a special case of Rydberg’s
equation where n2 = 2. Because of this,
the spectral lines described by
substituting n2 = 2 into Rydberg’s
equation are known as the Balmer series.
So the spectral lines were now mathematically
understood, however there was no theory explaining
why atoms produced emission and absorption
spectra.
This was one of the great successes of the Bohr
model.
Bohr’s Atom
http://youtu.be/hpKhjKrBn9s
This is not Bohr-ing
In 1913 Bohr produced a model of
the atom that both dealt with the
problems of the Rutherford model
and explained atomic spectra.
Bohr examined evidence collected
by other scientists and recognised
the connection between Balmer,
Planck and Einstein.
He combined their ideas and
predicted that Planck’s blackbody
oscillators were electrons, that
quanta were involved with
electrons transferring from one
energy level to another, and that it
was these quanta which
determined spectra.
Bohr’s Postulates
Electrons revolve only in
certain “allowed” orbits.
Bohr theorised that there
are a series of orbits, at
fixed distances from the
nucleus, in which an
electron will not constantly
emit radiation as demanded
by classical theory.
2.
Electrons gain or lose energy to “jump” between orbits. To jump up to
a higher orbit, an electron must gain a certain quantity of energy. If it
drops back to lower orbit, it must emit that exact same amount of
energy.
These quantities of energy are “quantised”, so each orbit is really a
“quantum energy level” within the atom.
The amount of energy absorbed or emitted during a “jump” is defined
by Planck’s Equation E = hf, and the corresponding wavelengths of light
are defined by the Rhydberg Equation. The integer numbers nf and ni
turn out to be the “quantum numbers” of the orbits, counting outwards
from the nucleus.
The energy that is absorbed or released as
electrons move between energy levels
explains why elements emit and absorb
radiation of specific wavelengths.
The energy levels for all the hydrogen
atoms in a sample of hydrogen gas are
identical.
When an electron in the second energy
level absorbs a photon of the right
wavelength it will gain the energy it needs
to move into the third energy level.
Therefore, photons at this wavelength will
be absorbed by the electrons in the second
energy level and will not be transmitted
through the hydrogen.
This wavelength will be omitted and a
black line will appear in the absorption
spectrum.
When an electron in the second energy level emits a
photon of the right wavelength it will move into the
first energy level.
The photons emitted will appear as a line in the
emission spectrum of hydrogen.
Rydberg’s equation relates the wavelength of the
photons to the changes in energy level of the
electrons. Therefore, it can be rewritten as
where ni indicates the initial energy level of the
electron and nf indicates the final energy level of the
electron.
In fact, all spectral lines for hydrogen can be
explained in this way.
Back to Hydrogen (Again)
Bohr’s explanation of the Balmer
series was that if an electron fell
from a higher shell down to shell
2, the spectrum emitted was
known as the Balmer series.
The Balmer series was in the
visible spectrum. There are names
given to the spectra when
electrons fall from higher shells
down to each of the shells.
For example, when electrons fall
to the first shell the spectrum
emitted is known as the Lyman
series which is in the ultraviolet
spectrum.
Summary: Bohr’s Postulates
1 Electrons exist in stable orbits. An electron can exist in any of
several special circular orbits with no emission of radiation.
These orbits are called stationary states.
2 Electrons absorb or emit specific quanta of energy when
they transition between stationary states (orbits). In
contradiction to classical electromagnetic theory, a sudden
transition of an electron between two stationary states will
produce an emission or absorption of quantised radiation (a
photon), described by the Planck–Einstein relation.
3 Angular momentum of electrons is quantised. An electron in
a stationary state (orbit) has a quantised angular momentum
that can take only values of
where n is the principal quantum number.
Questions on Rydberg
Nothing’s Perfect
The Bohr model was clearly a step towards an
accurate atomic model and not a completely accurate
model in itself.
It was limited in its application, contained
inconsistencies, and could not explain some
phenomena.
The Bohr model of the atom was specifically developed with
hydrogen in mind; it succeeded in explaining the hydrogen
spectrum. However, when it was used to try to explain the
spectra of·other elements several problems emerged.
The primary reason was that hydrogen has only one electron
orbiting the nucleus (in its neutral form). All other elements
have multiple electrons orbiting the nucleus (when they are
neutral).
As all electrons are negative the electrons repel each other.
In larger atoms an effect known as 'screening' occurs. The
inner electrons screen the outer electrons from the
positively charged nucleus.
As a result, the outer electrons do not feel all the positive
charge. The Bohr model does not take into account this
interaction and so cannot predict the spectral lines of large
atoms with many electrons.
The Bohr model also cannot
predict or explain the relative
intensity (brightness) of spectral
lines.
There are several laws in
quantum mechanics that forbid
certain transitions between
orbits. Rules known as the
selection rules allow certain
transitions to go ahead but
forbid or suppress others.
The allowed transitions showed
up in spectra with brighter or
more intense spectral lines and
at the time, this could not be
explained by the Bohr model as
the selection rules were not
known.
Bohr was also unable to predict the hyperfine structure seen in
atomic spectra, even for hydrogen.
Hyperfine spectral lines are faint, thin lines that exist as a cluster
around a main spectral line.
This splitting of the spectral lines comes about because of the
interaction between the angular momentum of the protons and
the electrons.
Bohr did not know this at the time so the model could not explain
these spectral observations.
As the electrons circulate the nucleus
they create a magnetic field. Any moving
charge creates a magnetic field.
When an external magnetic field is
applied to the atom this adds to the
magnetic field caused by the motion of
the electrons.
The interaction of the electron with this
altered magnetic field produces a
different energy to that produced when
the external magnetic field is turned off.
This changes the spectrum produced by
the atom by causing the spectral lines to
split in the presence of an external
magnetic field (known as the Zeeman
effect). Bohr did not consider atoms and
their magnetic fields in his model.
End of Focus Area 1