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The Wave Nature of Matter
Everything is made of particles. Pieces of solid matter. All solids, liquids, and gases – you name it. Dirt, pebbles, and red blood cells. Trees, dust mites, planets, and even the air we breath.
That’s obvious and common sense. We even make models of atoms and molecules with wood or plastic manipulatives like this, so that must mean something, right?
Except… we’re going to learn that all solid particles in the universe have a wave-like behavior.
And oh yes, all wave-like behavior has particle-like behavior?! Yup. For real.
This is the inescapable – and verified – result of the quantum mechanical nature of our world.
In the late 19th and early 20th century, when physicists asked hard questions about matter, they came across unexpected, extraordinary results.
We basically went through Alice’s Looking Glass – into the quantum realm. A realm where all particles have wave-like qualities. And further, all waves have particle-like qualities.
To be clear, none of this is a metaphor – we’re being quite literal.
The classical model of matter
The old model of the atom, and of everything in the universe was classical:
Everything is made of solid matter.
Everything has a definite position, mass, and velocity, at any moment in time.
Everything has a definite momentum at any moment in time.
How could it not? That seems to be true by definition.
We envisioned that there was a positively charged nucleus in the center of atoms.
Electrons (hence e– ) orbited around the nucleus like planets orbit around a start.
And so was everything else in our universe. People, cars, rocks, planets, and stars.
But when we looked more closely at their behavior, we kept seeing evidence that this model couldn’t be correct.
The classical model of atoms was wrong
e– lose energy by giving off photons (particles of light)
e– gain energy by absorbing a photon (and its energy)
If e– behaved like solid objects then they could move to any position (further from nucleus, or closer.)
They should be able to have any amount of energy: From a little to a large amount – and any value in between.
Therefore, when atoms gave off light, it was when e– dropped from one energy level to another.
If e– e could exist at any level then they could emit any energy of light, any color.
Thus atoms should be able to produce a continuous spectrum. Continuous means “all possible colors, smoothly going from one to the next, with no gaps.” Like this:
But experiments always showed otherwise! When individual atoms absorb light (energy) they only absorb photons (particles of light) in certain wavelengths. Yet they never absorb energy in others? How is that possible?
And when individual atoms emit (give off) light (energy), they only give off photons in certain wavelengths, never any others. Again, how is this possible?
No one could come with up with any model of the atom which was consistent with classical physics.
By 1913 Niels Bohr realized that nature was telling us something: Our classical intuition about what an atom was, was simply wrong.
We were forced to listen to what nature was telling us. Out of almost desperation, Bohr listened to nature and created a new, semi-classical model of the atom:
Like the old model, Bohr’s model portrays atoms as having a nucleus in the center and e– orbiting around it.
But in his new model e– could only exist in orbits of a certain radius. Not in any others.
Sure, they could lose energy, and “fall” from one orbit to a lower orbit – yet they didn’t exist anyplace in between?!
It was like they disappeared from kind of orbit – and reappeared in a different one?!
Quantum jumps
In classical physics any orbit is possible. It doesn’t make sense that only some orbits would be “allowed.”
Think of climbing a ladder. You can climb up from one stair to the next stair… and in doing so you obviously must pass all of the positions in-between.
There are an infinite number of positions between one ladder rung and the next. We don’t just disappear at one rung and then appear up at the next one, right?
(This GIF might be by artist Daniela Sherer)
This guy climbing the ladder, above, shows the classical, normal world we know.
We’re at one place, then at another – but only because we pass through every position in between.
The same thing goes for a car driving down the road. It starts at one place, ends up at another – and by definition the car must pass through every position in between.
But now imagine seeing this: the car literally disappears from the universe at one place, and then reappears in another place further down the road.
Animation by RK
Without ever being in any of the positions in between?! That’s not possible, right?
Except – that is precisely what e– in atoms seem to do.
Worse, all sub-atomic particles have this quantum leap type of behavior.
This violates common sense. But here’s the kicker – when we look closely, this is how the universe works.
Bohr’s model of the atom
An e– gives off energy in the form of a photon. Photon shown as green squiggly arrow.
Then the e– disappears from where it was and reappears in a lower orbit – without traveling through any position in-between!
Later, the e– absorbs energy from a different photon (another green squiggly arrow.)
Once it absorbs the energy the e- jumps up to a higher orbit – again, without traveling through any of the position in between.
These seemingly impossible jumps are called quantum leaps.
(FYI, e- do not actually circular orbits. Bohr’s model was just the first approximation)
(image Bohr atom animation.gif)
This model was the beginning quantum mechanics.
From the Bohr model to the wave model
The following Socratic-style discussion comes from Physics 2000.
Why should an electron’s angular momentum have only certain values?
Why do electrons emit or absorb radiation only when they jump between energy levels?
Bohr’s theory fits experimental results, but it doesn’t explain why atoms behave the way they do.
In 1923, about ten years after Bohr published his results, Louis de Broglie came up with a fascinating idea to explain them: all matter, he suggested, actually consists of waves.
At first, de Broglie had no idea what he meant by matter being “waves.” It was just a mathematical construct that was helpful.
It was only later that physicists realized that this mathematical construction was telling us something about the true nature of reality itself!
de Broglie’s wave model of particles explains why an electron can only be in certain orbits!
de Broglie’s wave model assumes that any particle – an electron, atom, bowling ball, whatever – had a “wavelength”
Yeah, that’s weird – but let’s just roll with it for the moment.
Why assume such a thing? This assumption wasn’t arbitrary; de Broglie knew that the momentum and wavelength of a photon actually were related.
Hmm, wait a minute…photons don’t have any mass, do they? How can photons have momentum?
Photons don’t have mass, but they do have energy – and as Einstein famously proved, mass and energy are really the same thing.
So photons do have momentum – but what exactly is a photon?
For centuries, a heated debate went on as to whether light is made up of particles or waves.
In some experiments, like Young’s double slit experiment, light clearly showed itself to be a wave.
But other phenomena, such as the photoelectric effect, demonstrated equally clearly that light was a particle.
So which is it? Well, sort of both – or better, it is neither.
Light is a thing that sometimes has particle-like behavior, and sometimes has wave-like behavior.
It all depends on what sort of experiment you’re doing.
This is known as wave/particle duality. Like it or not, physicists have been forced to accept it.
That’s why we sometimes talk about “electromagnetic waves” and sometimes about “photons.”
de Broglie’s big idea was that maybe it’s not just light that has this dual personality; maybe it’s everything!
All right…let’s say I accept this idea. How does it explain Bohr’s energy levels?
If we think of electrons as waves, we change our whole concept of what an “orbit” is.
Instead of having a particle whizzing around the nucleus in a circular path, we’d have a wave existing around the whole circle.
Now, the only way that such a wave could exist is if the wave has constructive interference.
It has to have a whole number of its wavelengths fit exactly around the circle.
If the circumference is exactly as long as two wavelengths, say, or three or four or five, that’s great, but two and a half wavelengths won’t cut it.
If we have fractional amounts of wavelengths then there is destructive interference, and the waves cancel out.
So there could only be orbits of certain sizes, depending on the electrons’ wavelengths –which depend on their momentum.
Apps: Modeling electrons with standing waves
Standing waves in Bohr’s atomic model
Standing waves in Bohr’s atomic model Geogebra.org
How to run CDF demonstrations: worlds of math & physics
Seeing constructive & destructive wave interference in 3 dimensions with DESMOS
More from Physics 2000
Student: But is this just some mathematical trick that happens to work, or do particles actually behave like waves sometimes?
Teacher: They actually do behave like waves! Just a few years after de Broglie published his hypothesis, several experiments were done proving that electrons really do display wavelike properties.
Student: So how come when I look at a bowling ball, I don’t notice it acting in a wavelike manner? You said that everything is affected by wave/particle duality.
Teacher: Think about what the wavelength of the bowling ball would be. According to de Broglie, the wavelength is equal to Planck’s constant divided by the object’s momentum.
Planck’s constant is very, very, very tiny, and the momentum of a bowling ball, relatively speaking, is huge.
If you had a bowling ball with a mass of, say, one kilogram, moving at one meter per second, its wavelength would be about a septillionth of a nanometer.
This is so ridiculously small compared to the size of the bowling ball itself that you’d never notice any wavelike stuff going on.
That’s why we can generally ignore the effects of quantum mechanics when we’re talking about everyday objects.
It’s only at the molecular or atomic level that the waves begin to be large enough (compared to the size of an atom) to have a noticeable effect.
Student: If electrons are waves, then it kind of makes sense that they don’t give off or absorb photons unless they change energy levels.
If it stays in the same energy level, the wave isn’t really orbiting or “vibrating” the way an electron does in Rutherford’s model, so there’s no reason for it to emit any radiation.
And if it drops to a lower energy level… let’s see, the wavelength would be longer, which means the frequency would decrease, so the electron would have less energy.
Then it makes sense that the extra energy would have to go someplace, so it would escape as a photon–and the opposite would happen if a photon came in with the right amount of energy to bump the electron up to a higher level.
Teacher: Very good! Now we can look at how Schrödinger extended de Broglie’s idea of waves into a whole new model for the atom…
What happened next, to finally create Quantum Mechanics, was that Schrödinger extended de Broglie’s idea of waves into a whole new model for the atom.
Related apps
Models of the Hydrogen Atom – PhET
Run this PhET app. Click to change from Experiment to Prediction. Press button to start the electron gun.
Under ‘Atomic model,’ the models of the atom most pertinent to this lesson are the Bohr model and the de Broglie model.
External resources
astronomy.nmsu.edu/agso/spectroscopy.pdf
Continuous spectra vs actual spectra
Emission Spectra: How Atoms Emit and Absorb Light
Emission and absorption spectra
Spectral Classification of Stars
Formation of Spectral Lines, Lumen
Physics 2000. University of Colorado by Prof. Martin V. Goldman. This website no longer exists except as an archived copy.
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Thanks for reading. While you’re here see our other articles on astronomy, biology, chemistry, Earth science, mathematics, physics, the scientific method, and making science connections through books, TV and movies.
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Maxwell’s Equations
Introduction
On Quora, Mark Eichenlaub writes –
The history of electromagnetism is one of unification. Over and over, different ideas about how things work were subsumed into the same theoretical framework…. Electromagnetism is an example of a field theory, the central object of study in theoretical physics.
A “field” means that at any point in space and time, there’s an electric and magnetic vector there. These fields pervade all of space – they are in the room around you right now, and in outer space, even within you…
We don’t have a mechanical picture of what the field is, or why it is a certain way. It’s not like waves in the water or anything like that. It just exists, but we do have mathematical rules that describe how it works….
Michael Faraday investigated things like the way a wire carrying electric current deflects a compass needle. His crowning achievement was to discover that changing magnetic fields create electric fields, a phenomenon called induction.
James Clerk Maxwell looked at all that, sat down with pen and papers, and mathematically described Faraday’s results in a complicated set of differential equations, importantly including the idea that changing electric fields would create magnetic fields, completing the symmetry between the two.
When Maxwell finished his theory, he discovered that it allowed waves of electromagnetism to fly off at high speed – when he calculated the speed, it turned out to be the speed of light.
Experiments with radio waves soon verified that light was nothing more than a special form of electricity and magnetism.
You can think of it as if we had been studying the way hot air balloons and airplanes and things work, and so were thinking about the dynamics of air. In the process, we develop equations for air, and figure out that sound is just waves moving through the air.
The theory of sound and the theory of airplanes are actually the same theory, even though they don’t seem very similar. That’s roughly what happened for light, except that unlike for sound, no one expected it. (Or at least it wasn’t obvious beforehand.)
Maxwell’s equations describe how electric and magnetic fields work, but those fields need to interact with matter – that happens via electric charge. Charge is an innate property of matter…
Fields
We keep talking about the electromagnetic field. What exactly is a “field” anyways? See What are fields?
Our articles
Maxwell’s equations (our main article, for now)
Backup: Get to know Maxwell’s Equations
External articles
Get to Know Maxwell’s Equations—You’re Using Them Right Now, Wired
Thanks for reading. While you’re here see our other articles on astronomy, biology, chemistry, Earth science, mathematics, physics, the scientific method, and making science connections through books, TV and movies.
Universal Design for Learning (UDL)
UDL is a design framework for providing increased access and reduced barriers to learning.
UDL encourages us to be intentional in our design without adding excessive demands on faculty. Many of us are already implementing good teaching practices that are the basis of universal design.
UDL can involve high-tech, low-tech and no-tech strategies.
Image by Gerd Altmann, Pixabay, Free for commercial use
Engagement – motivating students
Offer both group and individual work
Engage in-class and online
Allow students to select topics within a given assignment that is based on their interest and relevancy
Presenting information
Offer visual and auditory (text, video, visuals, infographics) works
Provide clear, detailed directions and instructions with rubrics and examples
Record lectures for review after class
Ways to demonstrate learning
Offer flexibility and choice in ways in which students demonstrate learning outcomes (e.g. presentation, essay, show step-by-step problem solving on a whiteboard, etc.)
Provide opportunities for feedback and revision of work
Increase amount of “low stakes” assignments
How teachers transform these ideas into action
Scaffolding: Making the standard curriculum and assignments more accessible.
* study guides
* tapping into student’s prior knowledge
* many opportunities to ask questions
* frontloading selected vocabulary
* relating ideas with analogies and visualizations
* Clear instructions and expectations.
* Frequent checks for understanding
* Have students use interactive apps
* Guided notes
* Graphic organizers
* Showing students how to color code notes, diagrams, etc.
* Historical, cross-curricular connections
* Recording lectures so students can review it later.
Differentiation: Providing a different level of curriculum and assignments. We adapt the topics covered to suit a student’s processing speed and ability.
* Text-to-speech (computer reads aloud documents to students)
* Speech-to-text (student dictates words and the computer writes them in a document.)
* Material from alternative textbooks. Offer a reduced wordcount and embedded vocabulary support for reluctant or struggling readers.
* Use a teacher-developed website: Utilize step-by-step explanations, color graphics, and interactive apps from a variety of sources.
* Shorter homework assignments.
* extra time for assignments
* Mastery grading
* Offer option for units to be self-paced.
* Replace traditional written lab directions with less text and more step-by-step diagrams/drawings.
Provide multiple ways for a student to show what they have learned
Draw – create a comic strip to show a process.
Create a PowerPoint (or Google Slide presentation)
Record a podcast or video (easy with iPads or Chrome extensions like Screencastify)
Create a commercial or skit
Create a concept map
For mathematics and physics problem-solving, it is essential for students to understand and use mathematical equations, and to use and create carefully labelled diagrams. Traditionally students use a pencil, paper, and calculator to do such work, fully writing out solutions on a sheet of paper. This process can be adapted for special education. I will write up a section on how this can be done in a physics class.
Thanks for reading. While you’re here see our other articles on astronomy, biology, chemistry, Earth science, mathematics, physics, the scientific method, and making science connections through books, TV and movies.
Fun books to inspire science teachers as well as students
Fun books to inspire science teachers as well as students
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Gonzo Gizmos: Projects and Devices to Channel Your Inner Geek, by Simon Quellen Field
Step-by-step instructions to building more than 30 fascinating devices …e.g. how to construct a simple radio with a soldering iron, a few basic circuits, and three shiny pennies. Instructions are included for a rotary steam engine that requires a candle, a soda can, a length of copper tubing, and just 15 minutes. To use optics to roast a hot dog, no electricity or stove is required, just a flexible plastic mirror, a wooden box, a little algebra, and a sunny day. Also included are experiments most science teachers probably never demonstrated, such as magnets that levitate in midair, metals that melt in hot water, a Van de Graaff generator made from a pair of empty soda cans, and lasers that transmit radio signals.
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Physics, Fun, and Beyond: Electrifying Projects and Inventions from Recycled and Low-Cost Materials, by Eduardo de Campos Valadares
Build more than 110 projects that uncover the physics beneath everyday life! Most o are amazingly easy to build: all you’ll need are your everyday household tools and cheap (sometimes free) materials.
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Why Toast Lands Jelly-Side Down: Zen and the Art of Physics Demonstrations, by Robert Ehrlich
A collection of physics demonstrations that prove that physics can, in fact, be “made simple.” Intentionally using low tech and inexpensive materials from everyday life, Why Toast Lands Jelly-Side Down makes key principles of physics surprisingly easy to understand. After laying out the basic principles of what constitutes a successful demonstration, Ehrlich provides more than 100 examples.
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The Prism and the Pendulum: The Ten Most Beautiful Experiments in Science, by Robert Crease
We see the first measurement of the earth’s circumference, accomplished in the third century B.C. by Eratosthenes using sticks, shadows, and simple geometry. We visit Foucault’s mesmerizing pendulum, a cannonball suspended from the dome of the Panthéon in Paris that allows us to see the rotation of the earth on its axis. We meet Galileo – the only scientist with two experiments in the top ten – brilliantly drawing on his musical training to measure the speed of falling bodies. And we travel to the quantum world, in the most beautiful experiment of all.
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How Things Work: The Physics of Everyday Life, by Louis A. Bloomfield
Uses familiar objects to introduce basic physics concepts with real-life examples. For example, discussions of skating, falling balls, and bumper cars are included to explain the laws of motion. Air conditioners and automobiles are used to explore thermodynamics.
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The Way Things Work Now, by David Macaulay
Explainer-in-Chief David Macaulay updates the worldwide bestseller The New Way Things Work to capture the latest developments in the technology that most impacts our lives. Famously packed with information on the inner workings of everything from windmills to Wi-Fi, this extraordinary and humorous book both guides readers through the fundamental principles of machines, and shows how the developments of the past are building the world of tomorrow.
This sweepingly revised edition embraces all of the latest developments, from touchscreens to 3D printer…. What possible link could there be between zippers and plows, dentist drills and windmills? Parking meters and meat grinders, jumbo jets and jackhammers, remote control and rockets, electric guitars and egg beaters? Macaulay explains them all.
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Building Big, by David Macaulay
Why this shape and not that? Why steel instead of concrete or stone? Why put it here and not over there? These are the kinds of questions that David Macaulay asks himself when he observes an architectural wonder. These questions take him back to the basic process of design from which all structures begin, from the realization of a need for the structure to the struggles of the engineers and designers to map out and create the final construction. Macaulay engages readers’ imaginations and gets them thinking about structures they see and use every day — bridges, tunnels, skyscrapers, domes, and dams.
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Insultingly Stupid Movie Physics: Hollywood’s Best Mistakes, Goofs and Flat-Out Destructions of the Basic Laws of the Universe, b y Tom Rogers
Would the bus in Speed really have made that jump? -Could a Star Wars ship actually explode in space? -What really would have happened if you said “Honey, I shrunk the kids”? The companion book to the hit website (www.intui tor.c om/moviephy sics), which boasts more than 1 million visitors per year, Insultingly Stupid Movie Physics is a hilarious guide to the biggest mistakes, most outrageous assumptions, and the outright lunacy at work in Hollywood films that play with the rules of science.
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Don’t Try This At Home!: The Physics of Hollywood Movies, by Adam Weiner
A fresh look at the basics of physics through the filmmaker’s lens. It will deconstruct, demystify, and debunk popular Hollywood films through the scientific explanations of the action genre’s most dynamic and unforgettable scenes.
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The Cosmic Code: Quantum Physics as the Language of Nature, Heinz R. Pagels
One of the best books on quantum mechanics for general readers. Heinz Pagels, an eminent physicist and science writer, discusses the core concepts without resorting to complicated mathematics. He covers the development of quantum physics. And although this is an intellectually challenging topics, he is one of the few popular physics writers to discuss the development and meaning of Bell’s theorem. Anecdotes from the personal documents of Einstein, Oppenheimer, Bohr, and Planck offer intimate glimpses of the scientists whose work forever changed the world.
A reviewer on Goodreads notes – “Pagels assumes a lay audience, but one prepared, after single paragraphs of description, to thereafter carry the technical terms across the finish line. Unlike other popsci, he also favors technical description–albeit written in smooth, clear prose over metaphor… The commitment to not talking down to his audience is rather commendable…
[His] intellectual project [is] reconciling the impossibility of visualizing quantum processes with a remit to communicate the science to non-scientists who, lacking the requisite mathematical literacy, necessarily require metaphor, universal human logics, and everyday comparisons to grasp most science in the first place.”
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Quantum Reality: Beyond the New Physics, Nick Herbert
Herbert brings us from the “we’ve almost solved all of physics!” era of the early 1900s through the unexpected experiments which forced us to develop a new and bizarre model of the universe, quantum mechanics. He starts with unexpected results, such as the “ultraviolet catastrophe,” and then brings us on a tour of the various ways that modern physicists developed quantum mechanics.
And note that there isn’t just one QM theory – there are several! Werner Heisenberg initially developed QM using a type of math called matrix mechanics, while Erwin Schrödinger created an entirely different way of explaining things using wave mechanics. Yet despite their totally different math languages – we soon discovered that both ways of looking at the world were logically equivalent, and made the same predictions. Herbert discussed the ways that Paul Dirac and Richard Feynman saw QM, and he describes eight very different interpretations of quantum mechanics, all of which nonetheless are consistent with observation…
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In Search of Schrödinger’s Cat: Quantum Physics and Reality, John Gribbon
“John Gribbin takes us step by step into an ever more bizarre and fascinating place, requiring only that we approach it with an open mind. He introduces the scientists who developed quantum theory. He investigates the atom, radiation, time travel, the birth of the universe, superconductors and life itself. And in a world full of its own delights, mysteries and surprises, he searches for Schrodinger’s Cat – a search for quantum reality – as he brings every reader to a clear understanding of the most important area of scientific study today – quantum physics.”
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The Elegant Universe: Superstrings, Hidden Dimensions, and the Quest for the Ultimate Theory, Brian Greene
“Brian Greene, one of the world’s leading string theorists, peels away the layers of mystery surrounding string theory to reveal a universe that consists of eleven dimensions, where the fabric of space tears and repairs itself, and all matter—from the smallest quarks to the most gargantuan supernovas—is generated by the vibrations of microscopically tiny loops of energy….
Today physicists and mathematicians throughout the world are feverishly working on one of the most ambitious theories ever proposed: superstring theory. String theory, as it is often called, is the key to the Unified Field Theory that eluded Einstein for more than thirty years.
Finally, the century-old antagonism between the large and the small-General Relativity and Quantum Theory-is resolved. String theory proclaims that all of the wondrous happenings in the universe, from the frantic dancing of subatomic quarks to the majestic swirling of heavenly galaxies, are reflections of one grand physical principle and manifestations of one single entity: microscopically tiny vibrating loops of energy, a billionth of a billionth the size of an atom.”
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Thanks for reading. While you’re here see our other articles on astronomy, biology, chemistry, Earth science, mathematics, physics, the scientific method, and making science connections through books, TV and movies.
How to Make a Topographic Salad-tray Model
What is a topographic map?
Here’s a topographic map of Pawtuckaway State Park (NH) It’s obviously an overhead view – but what do all these reddish contour lines tell us?
If we walked along one of these lines, we’d always be staying at exactly the same altitude. If we walked perpendicular to the lines, we’d be increasing/decreasing our elevation.
Consider this map of Nashoba Hill in Massachusetts.
Water always flows downhill, hence rivers are always perpendicular to lines on the topographic map.
When map lines are close together, the slope is steep, e.g. a cliff
How do we make a topographic map? Compare the overhead view with the side profile view.
Here are some topographic map examples.
Topographic maps 3D computer model: Class Zone
Topographic maps 3D – Second example: Class Zone
Mount Washington 3D Topographical Map Animation
White Mountain National Forest 3D Topographical Map Flythrough Animation
New Hampshire White Mountains Rivers 3D Map Animation
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This next part of the lesson/lab is from the United States Geological Survey (USGS,) How to Make a Topo Salad-tray Model
1. Select a feature that you would like to model. Islands work well because they have well-defined boundaries.
Mountains, canyons, or any feature with enough topographic relief will work.
2. Get a topographic map of the feature you want to model. Digital topographic maps can be created free from the USGS National Map at
USGC nationalmap.gov map viewer
3. Get some clear plastic take-out containers lids (any clear, stackable plastic with a flat surface will do).
You will need at least 7 or 8 plus a few extras in case of mistakes. They can be purchased at restaurant supply stores or any business that uses them for salads and take-out food. Or save them from your meals. Square lids are easier to work with than round.
4. Use a reducing/enlarging photocopier to adjust the size of the feature you are modeling so it is almost as large as the flat bottom of the plastic salad tray.
5. Once you have the correctly sized photocopy, use a marker to darken just those contour lines you want to transfer to the salad trays. In picking the contour lines to transfer, remember two things:
The difference in elevation between adjacent pairs of contour lines should always be the same. This difference is called the contour interval. The contour interval for the darkened lines on the back of this page for Angel Island, California is 100 feet.
The models seem to work best if you use a total of 7 or 8 contour lines (one per salad tray).
6. Let’s call the photocopy with the darkened contour lines the “master copy.” Using scissors, trim the master copy so that it just fits the flat bottom of the inside of a salad tray.
Getting the fit as tight as possible will help you put the master copy in the same position in each salad tray, and this will help the contour lines on the salad trays line up properly.
7. Position the master copy in the bottom of a salad tray, with the darkened contour lines against the plastic. Secure with tape so the master copy won’t move while you are tracing.
8. Looking through the bottom of the salad tray at the master copy, use a permanent marker (black seems to work best) to trace one contour line onto the salad tray.
9. Remove the master copy and position it in a second tray. Trace another contour line onto the second salad tray.
10. Continue until you have a different contour line on each salad tray.
Add the name of the feature, a scale bar (showing how long a mile is, for example), and a north arrow on the top or bottom salad tray.
Label each tray with the elevation of the contour line on that tray. Stack them up and be amazed!
Sample map
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Learning Standards
Next Generation Science Standards
4-ESS2-2 Earth’s Systems – Analyze and interpret data from maps to describe patterns of Earth’s features. [Clarification Statement: Maps can include topographic maps of Earth’s land and ocean floor, as well as maps of the locations of mountains, continental boundaries, volcanoes, and earthquakes.]
National Geography Standards Index
Standard 1: How to use maps and other geographic representations, geospatial technologies, and spatial thinking to understand and communicate information.
1. Properties and functions of geographic representations—such as maps, globes, graphs, diagrams, aerial and other photographs, remotely sensed images, and geographic visualization. Therefore, the student is able to:
A. Identify and describe the properties (position and orientation, symbols, scale, perspective, coordinate systems) and functions of geographic representations, as exemplified by being able to – identify and describe the properties of a variety of maps and globes (e.g., title, legend, cardinal and intermediate directions, scale, symbols, grid, principal parallels, meridians) and purposes (wayfinding, reference, thematic).
College Board Standards For College Success: Science
ESH-PE.1.3.1 Analyze earthquake data to find patterns in earthquake behavior and location.
ESH-PE.1.3.1a Locate, using latitude and longitude, earthquake data on a map.ESH-PE.2.1.1 Locate, by latitude, different zones of global atmospheric circulation patterns, and describe how these patterns interact with ocean systems on Earth.
ESH-PE.2.2.2a Explain why Earth’s surface heats unevenly at different locations due to variables such as albedo, latitude and surface cover.
ESH-PE.2.4.1 Explain climatic conditions in different locations, in terms of latitude, elevation, local topography and distance from large bodies of water.
Common Core ELA History/Social Studies
CCSS.ELA-LITERACY.RH.6-8.7 . Integrate visual information (e.g., in charts, graphs, photographs, videos, or maps) with other information in print and digital texts.
How can we see photos taken in UV, Infrared or Radio?
How is it possible that we can see photos taken in UV, Infrared or Radio?
Humans can only see visible wavelengths of light. Visible light has 𝜆 (wavelengths) of about 380 to 700 nm (nanometers.)
Yet in science class we often see infrared photos, like this!
Or we see photos taken in ultraviolet light. Bees see UV light, and so see flowers differently than we do. On the left is a primrose in visible light, but on the right we see it in UV light.
We see radar images of the Earth from an orbiting satellite, or radio telescope images of the galaxy. And those wavelengths of light just aren’t visible to humans.
UV light 𝜆 = 100 to 400 nm.
Infrared light 𝜆 = 700 nm to 1 mm
Radio waves 𝜆 = 1 millimeter to 100 kilometers.
Okay, the easy part is the technology: we can build equipment that detect such wavelengths. But what is the resulting image that we are looking at? Something visible to the human eye – which is in the visible spectrum.
So what does it even mean to translate something invisible to something visible?
Think about transposing music on a piano. We can play a melody in the middle of a piano keyboard. Then we can play the exact same melody one octave higher just by moving our hands to the right. We can do this again, and again. Each time the same melody is preserved, just an octave higher.
We can keep doing this until the notes are so high pitched that human ears can’t detect them (although maybe dogs and bats could hear this.) The resulting melody would be the same as the original melody, yet undetectable to us.
We can compare this to “seeing” higher frequencies of light – they get higher and higher until they become ultraviolet or X-rays.
Now, we can do the same thing again, but in reverse. Play a melody in the middle of a piano keyboard. Then we can play the exact same melody one octave lower just by moving our hands to the left. We can do this again, and again. Each time the same melody is preserved, just an octave lower.
We can keep doing this until the notes have such a low pitch that human ears can’t detect them (although whales, elephants, and hippopotamuses could hear this.) The resulting melody would be the same as the original melody, yet undetectable to us.
This is pretty much what is happening when we print out images of data capturing UV, Infrared or Radio!
For high frequency images (like UV light) we are dropping the image by many octaves (so to speak) until we reach the visible spectrum.
For low frequency images (like radio or infrared) we are increasing the image by many octaves (so to speak) until we reach the visible spectrum.
Avoiding misunderstandings
Electromagnetic waves (light, UV, radio) are transverse waves. The direction of particle displacement is perpendicular to the direction of movement.
Sound waves are longitudinal waves.
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Lava flows
Lava is molten rock (magma) that has been expelled from the interior of a planet, like Earth, Mars, or Venus.
The interior of such planets is very hot; this heat is left over from the creation of the planet billions of years ago.
Many people ask: how the world can still be so hot on the inside? For details see Why is the Earth still hot?
When this magma erupts through the crust of a planet, we call this lava.
Lava is usually between 700 to 1,200 °C (1,292 to 2,192 °F).
A “lava flow” is a fairly common phenomenon. We see this during a mostly non-explosive eruption. The lava soon cools to form igneous rock.
Lava is far more viscous than water, yet it can flow great distances before cooling and solidifying.
Several types of lava flows on land, and several types flow underwater/ocean
Lava flows on land
a’a (pronounced ah-ah) – Rough, rubbly surface because of their high eruption rates. As the upper surface of the lava cools and becomes rock, it is continually ripped apart by the moving molten lava inside the flow.
Pieces of the rocky surface are broken, rolled and tumbled along as the lava flow moves. When finally cooled to a solid, a’a lava flows look like a jagged heap of loose rock.
pahoehoe (pronounced pah-hoy-hoy) – relatively smooth surface texture because of their low eruption rates.
Pahoehoe lava flows develop surface crusts that form thick plates with ropy and/or gently undulating surfaces.
Pyroclastic flow
Pyroclastic flow in this section is not pure lava. Pyroclastic flows are mostly made of glass, ash, pumice, tephra (misc fragmented rocky pieces,) lava chunks, and hot gas.
Some lava does get sprayed up into the air and cools down quickly into falling rocks.
So the flow is like a battering ram of hot solid and gaseous material coming at you like a freight train.
From the USGS:
Pyroclastic flows move fast and destroy everything in their path. Heed evacuation warnings if a volcano is known to be active. If you witness a pyroclastic flow, run in the opposite direction as quickly as possible.
Pyroclastic flows move at very high speed down volcanic slopes, typically following valleys.
With rock fragments ranging in size from ash to boulders that travel across the ground at speeds typically greater than 80 km per hour (50 mph), pyroclastic flows knock down, shatter, bury or carry away nearly all objects and structures in their path.
The heat is between 200°C and 700°C (390 – 1300°F), can ignite fires and melt snow and ice.
Even relatively small flows that move less than 5 km (3 mi) from a volcano can destroy buildings, forests, and farmland. On the margins of pyroclastic flows, death and serious injury to people and animals may result from burns and inhalation of hot ash and gases.
This section is from Pyroclastic flows, USGS
How much lava can flow during these kinds of eruptions?
Here’s one example from Kīlauea, an active shield volcano in the Hawaiian Islands: Depth of the Halema‘uma‘u lava lake (2021)
Lava flows under the ocean
See these videos
A massive underwater volcano erupted and scientists almost missed it
Pillow lava flowing underwater off the coast of Hawaii
Undersea Volcano Eruptions Caught On Video (YouTube)
Stupendous Submarine Volcanoes (YouTube)
“Pillow” lava – forms rounded lumps that look like fat pillows. Can form piles a few to tens of meters high. Pillow lava flows can be many hundreds of meters to kilometers long.
Sheet flows – Form at much higher eruption rates than pillow flows. Rivers of lavas flow across the seafloor. These rivers can fill low areas in the seafloor and form lava ponds with very flat surfaces.
Lava in the ponds can also spread like thick pancake batter on a tilted grill, forming a long tongue-like flow. Sheet flows can have flat surfaces as well as twisted, ropy ridges all aligned in the direction that the flow moved across the seafloor.
Sheet flows exhibit a variety of surface textures.
Here is a lobate flow.
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Supervolcano
Supervolcano
A volcano which had an eruption of magnitude 8 on the Volcano Explosivity Index (VEI)
Such euprtions send out more than 1,000 cubic kilometers (240 cubic miles) of material.
These are exceedingly voluminous pyroclastic eruptions. They form monstrously huge calderas.
Few are recent. Most are ancient. Examples over the last couple of million years include the ones in Yellowstone National Park, Long Valley in eastern California, Toba in Indonesia, and Taupo in New Zealand.
There are large caldera volcanoes in Japan, Indonesia, and South America.
The most recent supervolcanic eruption on Earth occurred 27,000 years ago at Taupo, New Zealand’s north island.
…In 2005, BBC and the Discovery Channel produced a docudrama and documentary about Yellowstone called Supervolcano.
Below, Yellowstone Volcano Observatory scientists answer questions that arose after this program aired that relate to supervolcanoes, volcanic hazards, and Yellowstone.
The docudrama Supervolcano dramatically explores the impact of a large caldera-forming eruption at Yellowstone. The scale of the portrayed eruption is similar to the eruption of the Huckleberry Ridge Tuff at Yellowstone 2.1 million years ago.
The movie is realistic insofar as depicting what could happen if an eruption of this magnitude were to occur again. .. it does an acceptable job of addressing some of the issues scientists would grapple with if Yellowstone showed signs of an impending eruption.
Questions about supervolcanoes. USGS.
Comparing the volumes of eruptions
Regular eruptions are shown towards the right; super eruptions are shown towards the left.
Ancient supervolcano in Yellowstone Park
Yellowstone National Park is the first national park in the world – located primarily in the U.S. state of Wyoming, extending into Montana and Idaho. It known for its wildlife and its many geothermal features, especially Old Faithful Geyser.
See our article Yellowstone National Park & Caldera
Image by the National Park Service.
Yellowstone, one of the world’s largest active volcanic systems, has produced several giant volcanic eruptions in the past few million years, as well as many smaller eruptions and steam explosions. Although no eruptions of lava or volcanic ash have occurred for many thousands of years, future eruptions are likely.
In the next few hundred years, hazards will most probably be limited to ongoing geyser and hot-spring activity, occasional steam explosions, and moderate to large earthquakes. To better understand Yellowstone’s volcano and earthquake hazards and to help protect the public, the U.S. Geological Survey, the University of Utah, and Yellowstone National Park formed the Yellowstone Volcano Observatory, which continuously monitors activity in the region….
from Steam Explosions, Earthquakes, and Volcanic Eruptions – What’s in Yellowstone’s Future? U.S. Geological Survey Fact Sheet 2005-3024, 2005
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How do we know how atoms are arranged in a crystal?
How do we know how atoms are arranged in a protein, an enzyme, or a fat molecule?
Each individual atom is only a few nanometers (1 x 10-10 m) wide, way too small to photograph directly.
Yet we often see images of how atoms how are arranged, like this.
Just look it this image: We see individual atoms (yellow, red, blue) connected in a precise pattern. How in the world did we see this?
Well, there’s no way to see this, in one step. Too difficult.
But there is a way to accurately visualize this, if we go through a very careful process.
The process is called X-ray crystallography.
We start with a tiny sample of whatever it is we’d like to learn about. For example, a protein or an enzyme.
First, a biochemist needs to purify cells, and extract just the one molecule that we’re interested in.
That, in of itself, is a procedure that needs to be done carefully.
Once we have a pure form of that molecule, we then crystallize it.
Of course, in order for the rest of this lesson to make sense, we need to know what a “crystal” really is. So if you haven’t already learned about this, first check out our lesson on What is a crystal?
Short version: A crystal is solid material, in which the atoms, molecules, or ions are arranged in an orderly repeating pattern.
For instance, on the left is the atom-by-atom structure of a halite crystal.
(Purple is sodium ion, green is chlorine ion.)
This crystal is so tiny, that it would take 10,000 of them to make one tiny grain of salt!
On the right is a visible salt crystal. This contains millions of such crystal units.
Well, if we have a pure chemical from a cell (protein, enzyme, fatty acid, etc.) we can slowly cool and dry this chemical until it crystallizes!
Each different kind of molecule would create a differently shaped and colored crystal.
Please understand that these crystals look tiny – maybe just 1/10 of an inch across.
Yet each crystal contains millions of repeating atomic units.
Figure 22.3. Examples of protein crystals. From left to right: β-secretase inhibitor complex; human farnesyl pyrophosphatase in complex with zoledronic acid; abl kinase domain in complex with imatinib; cdk2 inhibitor complex.
Source – Jean-Michel Rondeau, Herman Schreuder, in The Practice of Medicinal Chemistry (Fourth Edition), 2015
This crystal is then placed in front of an X-ray source.
The X-rays scatter off the atoms in a crystal.
Those X-rays fly onto either a piece of film, or a digital X-ray detector plate.
Either way, we end up with a beautiful array of dots called a diffraction pattern.
This pattern is beautiful – but doesn’t seem to look like anything?
Ah, but there’s a relationship between the placement of the atoms, and where the X-rays deflect off of them – just like there’s a relationship between a pool ball bouncing off of other pool balls.
Think about it: If you know how a pool table is set up, what balls are made of, and see how the balls move after being it, then you could use math to work backwards.
Just by seeing the results of where the balls are scattering to, you could work backwards to figure out where the balls originally where.
from Banks and Kicks in Pool and Billiards, Dr. Dave Alciatore, Billiards and Pool Principles, Techniques, Resources
The same is true here: We can use math to figure out where each individual atom in the molecule is!
Let’s follow the steps below:
On the left, we see X-rays leave a source. Some of these x-rays hit a lead screen. All those X-rays are stopped.
Only a thin, focused beam of X-rays makes it thru the slit.
Those X-rays hit our crystal sample.
The X-rays bounce off the atoms, like pool balls bouncing off of each other.
(This GIF created by Abhijit Poddar, ‘E-learning’ of select topics in solid state physics and quantum mechanics)
Some of the x-rays bounce onto a film plate. This makes an image.
We end up with a diffraction pattern on film.
Figure 11.4, Purves’s Life: The Science of Biology, 7th Edition
Once we have a diffraction pattern, we use math to work backwards:
We figure out where the atoms must have been.
The result is an electron density map.
This traces out the shape of the atoms in the molecule.
Left image: X-ray diffraction pattern, Wikimedia. Right upper image: electron density map. Right lower image: model fitting atoms to the density map.
Appearance of a zone of the electron density map of a protein crystal, before it is interpreted
The same electron density map after its interpretation in terms of a peptidic fragment.
These last two images come from CSIC Crystallography
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External resources
Welcome to the world of Crystallography: The Spanish National Research Council
Cryo Electron Microscopy
Cryo-EM is an electron microscopy (EM) technique applied on samples cooled to cryogenic temperatures and embedded in an environment of vitreous water.
An aqueous sample solution is applied to a grid-mesh and plunge-frozen in liquid ethane or a mixture of liquid ethane and propane.
While development of the technique began in the 1970s, recent advances in detector technology and software algorithms have allowed for the determination of biomolecular structures at near-atomic resolution.
This has attracted wide attention to the approach as an alternative to X-ray crystallography or NMR spectroscopy for macromolecular structure determination without the need for crystallization.
Cryo-electron microscopy wins chemistry Nobel, Nature
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Geography, geology, geometry and geodesy
What’s the difference between geometry, geology, geography and geodesy?
Geometry
the branch of mathematics concerned with the properties and relations of points, lines, surfaces, solids.
Here is a very common example of what one may study in geometry.
In geometry we also learn about things like angles –
And of course geometry has many practical uses in many careers!
It is very useful when designing gears, drills bits, laying out camera lenses, and so much more.
from gear designs equations, engineersedge.com
Geology
This is the science that deals with the earth’s physical structure and substance, its history, and the processes that act on it.
Geology includes the study of minerals, crystals and rocks.
Geography
Geography is the the spatial study of Earth’s landscapes, peoples, places and environments.
This includes cartography (map-making.)
Here’s an example of how we use shadow projections in geography to create maps.
Of course, there are many types of maps used in geography.
Geodesy
Geodesy combines applied mathematics and earth sciences to measure and represent the Earth (or any planet.)
Isn’t the Earth a sphere? Well, mostly, sure. But exactly? No, not at all – and sometimes the actual difference matters quite a bit!
NOAA National Geodetic Survey, from a PPT by Hawaii Geographic Information Coordinating Council
Don’t we already know the Earth’s shape and size? To some degree, yes, of course. But how accurate? To the nearest plus or minus 100 feet? Plus or minus ten feet? Plus or minus one foot? Each decade, with new advances in technology, our measurements become more accurate.
And this matters because the Earth’s surface doesn’t always stay the same. Over time – even within a one year period – land can move up or down.
from the National Oceanic and Atmospheric Administration Ocean Service Education page on Geodesy:
KaiserScience 
