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.
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.
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.
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.”