S04E11: The Justice League Recombination

Many of you may have laughed at Zack tonight because he confused a picture of the Solar System with a model of the atom.   But, building on that similarity a century ago won Niels Bohr a Nobel Prize.

Is that represent a planetary system or an atom?

A planet, left alone, would travel in a straight line, at a constant speed, forever.  That observation is so important, it became Newton’s First Law:  “Every body remains in a state of rest or uniform motion (constant velocity) unless it is acted upon by an external unbalanced force.”  Like the Pioneer Spacecrafts launched in 1972 and 73, at our current speed we’d leave the Solar System behind in just a few decades.   So if  Earth  is traveling in near circles around the Sun,  then a force must be acting on it.   What could be simpler?  But actually there are a number of subtleties that trip up and sometimes even amaze our first-year physics students:

Newton’s second law says that a force, such as the attraction of gravity between the Sun and the Earth, causes a directly proportional change of acceleration:  “Force equals mass times acceleration”.  Acceleration is just a definition: a change in velocity per time.  When you say your car goes from “zero to 60 mph” in 10 seconds, that’s a description of its acceleration.  But the Earth’s speed changes by less than 2% from its average over the course of a year and its average has barely ever changed in over 4 billion years.    If our orbit were perfectly circular, it would not even change at all.   What happened to all that acceleration that the force must produce?   The missing point is that velocity is not just speed, but also direction.    Every  six months, the Earth completely changes its direction as viewed from the Sun.  In such a circular orbit, the acceleration changes the direction of the motion not its rate…so velocity is still changing.

Newton’s second law also says the acceleration points along the same direction as the force.   A common misconception is that the acceleration of the planet in circular orbit points along the direction of motion.   But the force of gravity points along a line between the Earth and Sun.  So the acceleration cannot be pointing along the direction of such a planet’s motion.  The acceleration must somehow point along the same line between the Earth and Sun.   That is, it points at right angles to motion along the circular orbit.   So  the planet changes direction but not speed and is still accelerating.  A planet in circular motion can be acted on by a force forever, but its speed and thus energy never change.

Richard Feynman put a fine point on it.  In the time of Kepler, many stated that the Earth moved because angels pulled the Earth along, flying ahead of the planet.   Newton showed us though that this model cannot be correct.   The angels must be pulling on us inward towards the Sun, thereby creating our (essentially) circular orbit.

Back in the early 1900’s, the existence of atoms, indivisible units of the known elements, was largely, and correctly, in favor.   What nobody knew, was the structure of an atom itself.  Theories abounded, that were all reasonable.    In the “plum pudding” model guessed by J.J. Thompson, the discoverer of the electron, there was an equal mix of positive and negative charges (protons and electrons) all mixed up uniformly in a kind of goo.  Not a bad guess but wrong.   Another model described atoms as cubes, with electrons at the corners.    A Japanese physicist, Hantaro Nagaoka, guessed a model with electrons surrounding a central positive charge arranged in a single disk, at a constant radius, much like a narrow ring of Saturn.

All these models were reasonable. In fact the plum pudding model turned out later not to be a bad explanation for the structure of the nucleus.   No amount of theoretical calculating would resolve the impasse.   It took an experiment to point the right way forward.  In Ernest Rutherford’s lab, evidence was seen that alpha particle (positively charged particles) scattered off of a densely packed solid nucleus.  So the  closest winner among the predictions above was the Saturn-like, or planetary model—which unfortunately predicted essentially nothing correctly.

Niels Bohr quickly refined that model to one with electrons orbiting a central nucleus at different distances.  He had the electrons orbit the central nucleus at a constant speed and distance, much like a planet, but with the force of gravity replaced by the force of static electricity between the (negatively charged) electron and (positively charged) nucleus.   He helped start quantum theory by assuming that, unlike planetary systems, electrons could only orbit the atom’s central nucleus at specific, fixed distances.

Experiment showed that Bohr’s model worked better than the Saturn model because it  explained the specific values of light frequencies emitted by atoms.   That left us with the picture of the atom so popular in popular culture, with little electrons zipping around a central nucleus just like planets around the Sun.

The planetary model of the atom is most familiar. It was the first to make good predictions. But it does not work completely.

Almost immediately physicists knew that Bohr’s planetary model of the atom could not be the final story.   It is a fact that accelerated electrons radiate power.   That is actually how a radio transmitter works, it accelerates the electrons in a metal antenna.   But since atoms can be stable forever, with their orbiting (accelerating) electrons, something was wrong.   Bohr finessed the issue by saying an electron could not move closer than a minimum radius.   But worse problems could not be solved.  An electron truly orbiting a central charge would do so in a particular direction, and therefore have angular momentum.  But experiments said otherwise, that it could even be zero.   No orbit around a central body can have zero angular momentum.

Ultimately the planetary model was killed by these disagreements with data.   Only the with advent of the full quantum mechanics, including the Shroedinger wave equation, could a picture be made consistent with all that was observed.   In this, better working, picture the lowest energy electrons exist in a kind of cloud around the nucleus, with nothing orbiting at all.  Unfortunately, when quantum mechanics becomes key, there is no familiar system, such as planets’ orbits, to compare it to.

In the modern picture of an atom, there are no orbits, just a cloud of probability of finding the electron.

Zack wouldn’t confuse a cloud of electron probability with a planetary system.   Since the planetary model of the atom is dead, one could even say his was a better guess than Leonard’s.

In a strange way Zack had a point when he said, “That’s what I love about science–there’s no one right answer.”    Science typically moves forward with multiple of guesses, such as the Saturn ring model of the atom.  Several explanations often  co-exist until experiments weigh in and pick some, one, or none.

No wonder Zack wants to “talk science with the science dudes.”

16 Responses to “S04E11: The Justice League Recombination”

  1. Paul Dushkind Says:

    “Is that represent a planetary system or an atom?” Neither, it’s a fried egg.

    Actually, Zack also didn’t ask such a dumb question weeks earlier when he asked why a laser didn’t blow up the moon. I’m not a scientist, but I believe that the correct answer is that it’s not a powerful enough laser (and also that the beam is too narrow). Now, is the truth really so different from Leonard’s facetious answer, “Because we set the laser on stun”?

    • David Saltzberg Says:

      I’m told that by those who do the experiment that one not uncommon response to the explanation that the laser is not powerful enough to blow up the moon is: “But why risk it?”

    • Ian Says:

      The power of the laser would definitely have to be much higher to detonate the moon, however a larger beam would decrease the intensity of the laser and would make it even more difficult. You want a small, focussed beam to get maximal intensity – like using a magnifying glass to fry ants.

      With a powerful and focussed enough beam, the laser would begin burning a hole through the moon – which would cause heating of the area around the focus – which would put pressure on the rest of the moon – which is what I think would cause it to explode (although more likely split into several large chunks rather than detonate like a Death Star blast from Star Wars).

      • feldfrei Says:

        @Ian: It is by far not easy to transfer enough energy to the moon in order to break it into pieces. Consider the size of the moon, the energy needed to melt (or even vaporize) rocks, thermal stress etc.
        Concerning the laser focus, also the distance to the moon (0.38 million km) and the diffraction limit are of relevance. In addition, high-power lasers usuallay operate in a pulsed mode such that the average power is rather low. Provided you have enough energy to vaporize significant amounts of rock on the moon’s surface an interesting effect may show up: due to the rocket-like repulsion of the emerging gas/plasma the moon’s orbit will change. It may be instructive to estimate the rate of evaporation needed for a significant change which can compete e.g. with the ongoing angular momentum and energy transfer to the moon due to tidal forces.

      • Brophy Says:

        Guys, Guys..
        Theory about how powerful a laser needs to be, what kind of laser or how it should function is beside the point…
        Have you any idea how big the hole in our atmosphere you would create?! the Ionosphere is so named for a reason (not to mention our old friend the ozone layer..)

        Otherwise my idea about an energy delivery system from Solar Satellites in Geosynchronous orbit via laser would have been patented long ago…
        how I envy Alternate Universe me..

  2. steve Says:

    wouldnt a laser just melt the moon?
    unless it hit something explosive?

    • Ted Seeber Says:

      “wouldnt a laser just melt the moon?”

      Only if your moon is made out of green cheese 🙂

      Still, this back and forth of many right answers, reminded me of a recent article in the New Yorker being passed around that is frightening many “social scientists” and not a few “hard scientists” as well: The Decline Effect:

      Which seems to me would make for a great episode of The Big Bang Theory; the fact that many scientific discoveries, due to a combination of very human factors subtlely influencing the data, become irreproducible after a relatively short timespan. Kind of a macro world example of the subconscious human mind in a very diligent but optimisitic scientist creating a macro-world Heisenberg Effect.

      And maybe other philosophical methods than the scientific method still have a place in the human search for truth after all.

  3. feldfrei Says:

    Thanks for this nice (and fundamental) example how models are developed in science and checked by experiment (which in turn has always to deal with errors – the hardest (and finally endless) game is to measure a zero effect). The discovery of spectral lines emitted by atoms opened access to cosmic chemistry but the physics behind these lines remained unclear for decades. Besides the angular momentum problem Bohr had to postulate that orbiting electrons (as an accelerated charge) do not radiate and if – then only during transitions between distinct quantum states. Schroedinger’s wave mechanics finally showed that there is some kind of “motion” but this happens not in real space but rather in the (imaginary) plane of complex numbers (a concept that is familiar to electrical engineers). The electronic wave functions rotate in the complex plane (with a frequency corresponding to the binding energy) and, thus, their absolute value squared – which gives the charge densitiy – becomes time-independent. Considering now a superposition of two quantum states one gets a beating frequency according to the energy difference of the states. An upper state decaying into a lower one is then described by a corresponding superposition which leads to a charge cloud oscillating with the transition frequency – and it radiates like a classical antenna.

  4. Yves Says:

    Given an infinite number of universes, there are an infinite number of universes in which Wonder Woman is a blonde.

  5. Jim Cliborn Says:

    Funny episode and very informative blog! At this point perhaps it would be good to post the five things Dirac would have one know about electrons. From

    SIAM News, Volume 36, Number 2, March 2003, we have:

    “Seventy-five years after Dirac’s breakthrough, nearly every popular account of electron spin still describes electrons as if they were rotating billiard balls. And they are all equally wrong. Here are five reasons that this “mental picture,” as Dirac would call it, does not conform to reality:

    1. “Electron spin is quantized; the angular momentum of a classical billiard ball is not. Nothing can gradually “slow down” or “speed up” an electron’s spin.

    2. “The electron’s spin “axis” is completely reassigned by any attempt to measure it.

    3. “The electron’s magnetic moment is two times too large for a spinning ball of charge. (Or its spin is two times too small for its magnetic moment.)

    4. “If an electron were a spinning ball, the linear velocity of its surface would exceed the speed of light.

    5. “Quantum physicists know that an electron does not orbit a nucleus in the same way a planet orbits the Sun. So why should the electron rotate like a planet?”

  6. Zig zag zug Says:

    A nice blog post! I remember asking my high school chemistry teacher: “So… like a planet?” and getting a “…sure!” as an answer and a sudden look of horror as she gazed into something unseen far away.

    And Zack is good bloke, someone you can turn to for comfort, as Penny did it seems. Supposing he was never exposed to science as a kid (or that he has dyslexia or ADD), he might of gotten a sum total of a single science class in all his life that he barely passed… so he knows it’s about solving problems using “rules” and not reasoning. Later, he develops a pragmatic view: Do ‘X’ to get Y. That’s science! So… to blow up the moon, you use dynamite, a laser or some other X that gets you Y. Then he asks: “do you guys know other ‘X’s that do Y?” to which Leonard and co respond: fool, there is only one true ‘X’… It’s called “X = Y”.

    This is confusing! To Zack, there are many different X that give Y, but to Leo there is only the true action of “X = Y”. So, we seem to have an impasse. Leo sees a 1 to 1 function: send X amount to Y = blow up moon. How you do it doesn’t matter, as long as you get X = Y. For Zack, you get an ‘X’ to Y : apply laser or apply dynamite = blow up moon. Leonard would hear that and say: no, what your doing is applying energy. Anything that does equivalent work to blow up the moon can be exchanged without issue. E = mc^2, and all that good stuff!

    To which Zack would say: ya, but turning 1 laser into dynamite to blow up the moon costs money! To which Leonard says, wait, so E1 = mc^2 = blow up moon, and E2 = mc^2 = blow up moon, but E1 doesn’t equal E2? Something is added to the mix to create a difference between E1 and E2? So that you can never exchange E1 for E2 without noticeable differences?

    Then Zach’s eyes glaze over, and he says “uh… wait what?”

    hmm… I guess not all E’s are made equal. ^_^

    Sure, there’s only 1 tangible Universe, but, like a mythic Hydra, humanity looks at it from many angles? But some things seem more clear than others. Perhaps instead we are the equally ferocious but far sexier Medusa! Anywhooo…

    /Sheldon mode ON!
    A fact: there are now as many teachers in America as there are people with criminal records. Another fact: I see double spacing at the beginning of every sentence in this blog, but not others, so I conclude that a) the writer once used a typewriter, and b) he’s tired and distracted. Adding facts, I concluded that the writer of said blog should rest, and not worry so much about whatever because the Zacks need teachers now more than ever!
    /Sheldon off!

  7. Ted Seeber Says:

    And I’ve now closed the circle- I found the Decline Effect Article on the “Magis Center For Reason and Faith” wall on facebook- where I have now started a discussion on the Zero Effect Error:

  8. WBT founder Says:

    i love this ep. nice blog 😛

  9. Get Passed Says:

    Get Passed…

    […]S04E11: The Justice League Recombination « The Big Blog Theory[…]…

  10. pcmazwrupp@gmail.com Says:

    What are the rules of composing music? I have been creating both classical music and also dance music with?

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