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The Hydrogen Atom – the Key to Understanding Spectra:
1. Rutherford discovered in 1910 that the overwhelming bulk of
the mass of an atom is concentrated at its center in a very small
nucleus.
Bohr’s
model of the
hydrogen
atom.
2. This discovery led Niels Bohr, who joined Rutherford’s group
at Manchester in 1911, to build a simple conceptual model of
the simplest of all atoms, the hydrogen atom.
3. Bohr conceived of the hydrogen atom as a single electron
orbiting a nucleus consisting of a single proton.
4. He proposed that the electron could only have a series of
specific orbits, corresponding to specific orbital energies.
5. He proposed that when the electron jumps from one allowed
orbit to another, it either absorbs or emits a photon whose
energy equals the difference of the energies of the 2 orbits.
Bohr’s Model:
Bohr’s model of the hydrogen model is extremely simple, and
gives us a means of understanding how the spectrum of only
very special light wavelengths is generated.
In our modern understanding of the hydrogen atom, we think of
the electron as not having a specific orbit, like a tiny earth
going around a tiny sun, but as having a likelihood
(probabilit ) of being in an
(probability)
any one partic
particular
lar place near the
atom’s nucleus, its proton.
When the electron is in the state of lowest
energy, where it is most tightly bound to
the nucleus, the probability of finding it at
a given location depends only on that
location’s distance from the nucleus, as
shown here.
We can visualize this distribution of the likelihood of finding the
electron as an “electron cloud.”
In the lowest energy, or “ground,” state, the electron cloud has a
spherical distribution about the proton, as shown on the next
slide.
The ground state of the hydrogen atom:
Electron “degeneracy” and the size of a white dwarf star:
In Bohr’s model, with the electron orbiting the proton like the
earth about the sun, it is hard to understand how there can be a
“ground state.” It should, it seems, be possible for the electron
to get closer in toward the proton and become even more
closely bound.
We will see as we discuss stellar evolution that the end state of our
sun, billions of years from now when it no longer generates
heat inside itself, will consist of material pulled so strongly
together by gravity that it is held up by the fact that its
electrons cannot possibly get closer together. We can think of
the electrons in this “degenerate” state as essentially
“touching.” It is the electrons that “touch,” because they take
up much more space than the nuclei of the material
material, just as we
can see in the picture of the hydrogen atom on the previous
slide.
But in the modern view, where we think of the electron as an
“electron cloud,” we can see that it is not possible for the
electron
l
to get closer
l
to the
h proton than
h in
i the
h groundd state.
In the ground state, we can think of the electron as essentially
sitting right on top of the proton – it cannot get any closer.
In this view, the size of the electron cloud in the ground state of
hydrogen is the size of the electron itself. If we tried to push a
whole lot of hydrogen atoms together in a box, we could then
not make them take up less space than this. This consideration
will turn out to determine the size of a white dwarf star.
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In a transition from a higher energy state to the ground state of the atom,
as is shown here at one instant, the electron cloud is alternately
concentrated on one side or the other of the central nucleus. As the
electron cloud moves up and down, a wave of light – a photon – is
emitted which carries away the extra energy of the excited state.
For the transition shown here, each oscillation of the electron cloud takes
about a millionth of a billionth of a second (10-15 sec), and the transition
is over after about 10 million such oscillations. The wave train of light
that is emitted ( the photon) thus has about 10 million wavelengths.
www.hydrogenlab.de/
This set of diagrams is intended to illustrate how the motion of
a charge q1 causes the charge q2 to move due to the
electromagnetic force between them.
There is a slight delay required for the signal that the charge q1
has moved to reach the location of charge q2.
This signal travels at the speed of light, and in fact is light.
We can make an analogy with the wave in the surface of a lake that is
caused by a floating object bobbing up and down.
This motion will cause waves to radiate outward, and these will cause
objects floating elsewhere on the lake surface to bob up and down as the
waves pass by.
These water waves, like light waves, are “transverse” waves.
This means that objects are caused to move perpendicular to the direction
of the wave propagation as the wave passes by.
In the next slide, we show the propagating light wave caused by
the up and down motion of a charge, like the electron in a
hydrogen atom, as indicated at the middle of the picture.
The wave crests move outward at the speed of light (of course).
As they pass by, a charge along their path is caused to move up
and down, just as a cork floating on the surface of a pond moves
up and down as the crests of a water wave pass by it.
The wave is “transverse,” in that the motion induced is up and
down while the motion of the wave crests is in the horizontal
direction. Thus the induced motion is perpendicular to that of
the wave propagation.
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Here we make a comparison of transverse waves on the left, using waves
propagating along a string (like a violin string), with longitudinal waves
on the right, using compressional waves traveling along a spring
(sound waves in air work this same way).
We can think of what is oscillating along the direction of a light wave’s
path as the electric and magnetic fields.
The direction and amplitude of the electric field tells us the size and
direction of the electrical force that would be exerted upon any charged
particle located there. Thus charged particles along the light wave’s path
would be pushed upward or downward as shown by the vertical arrows.
We will not discuss the magnetic field.
From these diagrams we can see what we mean by the wavelength and
amplitude of a wave. The wavelength is the distance between wave
crests, and the amplitude tells us the height of the crests.
From these diagrams we can see what we mean by the wavelength and
amplitude of a wave. The wave propagation speed is also shown. It tells
us the speed with which the wave crests advance. The two waves at the
right travel with the same speed, but because the lower one has half the
wavelength, it has double the “frequency,” which is the number of wave
crests passing an observer per unit time.
The wave numbered 2 at the right has twice the frequency of the one
numbered 1 above it. A light wave of twice the frequency (half the
wavelength) but the same amplitude causes a charge it passes along its
path to move up and down twice as rapidly. This imparts more energy to
the charge, and we therefore see that the wave of higher frequency
(shorter wavelength) has more energy.
All light signals propagate at the same speed in a vacuum, and we call
this the speed of light. Light waves with different wavelengths (and
hence different frequencies) are given different names, as set out in this
diagram. Astronomers get information about objects in the sky from
light of all these different frequencies. We design special telescopes to
observe the different ranges of light wavelengths.
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Going back to Bohr’s simple model, we see that transitions of the
electron from the larger orbits, with higher energy, into the ground
state (the smallest orbit) cause the emission of light waves with
greater energy and hence higher frequency.
Going back to Bohr’s simple model, we see that transitions of the
electron from the larger orbits, with higher energy, into the
ground state (the smallest orbit) cause the emission of light
waves with greater energy and hence higher frequency.
For the hydrogen atom, the sequence of ever higher such energies
and frequencies of light is very simple mathematically.
This allowed Bohr to come up with his simple model.
Without the simple example of the hydrogen atom, we might never
have figured out how atoms really work.
A series of “spectral lines,” or specific wavelengths (or frequencies)
of light that can be emitted or absorbed by a hydrogen atom, are
shown at the bottom right on the next slide.
In one of your laboratory experiments, you will observe such
spectra for hydrogen and other elements such as sodium or neon.
On the following few slides, we see a number of spectra.
You will have a lab on this subject.
Here you can get an idea of the variety of spectra and also their
complexity.
The spectrum of an element, like hydrogen or sodium, is like its
fingerprint or its bar code. It is unique and can be used by a
trained person to positively identify the element.
Astronomers use these characteristic patterns of spectral lines in
the light of distant stars to determine the chemical composition
of those objects – a feat that would otherwise be impossible
without going to the distant star and analyzing its material.
The wealth of information in the spectrum of light from an object
is therefore a powerful tool for understanding the object.
Here we see emission lines of the spectrum
of the element mercury (Hg) under various
conditions.
Top:
Hg lamp at low pressure
Middle:
Fluorescent lamp and Hg lamp
Bottom:
Hg lamp at high pressure
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Electric lamp spectrum
Solar spectrum
Some absorption lines (dark bands) can be seen in the
continuous black body spectrum of the sun.
Solar spectrum
Aluminum oxide spectrum
Iron spectrum
Spectrum of candle light
Hydrogen
Neon
High pressure Xenon
Spectra from discharge tubes
Top: Sodium spectrum.
Middle: Sodium absorption in spectrum of incandescent light.
Bottom: No sodium absorption with low temperature incandescent light
What is it that we need to understand?
1. How we can use Newton’s theory of gravitation to find the
masses of planets, stars, and galaxies.
2. Energy conservation and some of its implications.
3. How gravitational potential energy is liberated when a massive
object gets smaller, and where this energy goes.
4 How
4.
Ho mass can be converted
con erted into energy
energ in other forms.
forms
5. How angular momentum conservation affects the rate of spin
as the radius from the rotation axis changes.
6. Quantized energy levels of atoms and molecules, and the
implications for spectra.
7. Doppler effect: spectral line shift and/or broadening.
8. Effect of temperature on spectrum.
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Fig. 7.16
Spectral
Lines
What is it that we need to understand?
1. How we can use Newton’s theory of gravitation to find the
masses of planets, stars, and galaxies.
2. Energy conservation and some of its implications.
3. How gravitational potential energy is liberated when a massive
object gets smaller, and where this energy goes.
4 How
4.
Ho mass can be converted
con erted into energy
energ in other forms.
forms
5. How angular momentum conservation affects the rate of spin
as the radius from the rotation axis changes.
6. Quantized energy levels of atoms and molecules, and the
implications for spectra.
7. Doppler effect: spectral line shift and/or broadening.
8. Effect of temperature on spectrum.
How do spectra change with temperature?
1. From the earlier discussion of blackbody spectra, it is clear that
as the temperature is raised, light of shorter wavelengths will
be emitted.
2. For a gas of hydrogen, for example, that is not opaque (not a
good absorber of light, and hence not a blackbody), an increase
in its temperature will result in more powerful emission of the
shorter wavelength lines in its spectrum.
3. This happens because the more violent collisions of the
hydrogen atoms caused by the high temperature of the gas
continually place electrons in the higher energy states from
which high energy (short wavelength) photons may be emitted
upon transitions to the lower energy states.
4. Thus the temperature of a gas through which a strong
continuous spectrum is shining may be estimated by the
relative strengths of its spectral lines.
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