MadSci Network: Physics

Re: Do electrons behave like satelites?

Date: Mon Dec 11 01:35:37 2000
Posted By: Vladimir Escalante-Ramírez, Faculty, Institute of Astronomy, National University of Mexico
Area of science: Physics
ID: 975783129.Ph

In 1913 the Danish physicist Niels Bohr formulated a 
model for the hydrogen atom that said that an electron 
moves around the proton in a way similar to the way 
a satellite moves around the Earth. The only difference 
is that the electron cannot exist in any orbit. Instead 
its angular momentum given by mvr (m times v times r), 
where m is the electron mass, v the velocity and r 
the distance of the electron to the nucleus must 
be equal to n times hbar where hbar is the Planck 
constant and n is any integer number from 1 to 
infinity, i.e., n=1,2,3,4,... When a physical quantity 
is limited to a discrete set of values, we say that it 
is "quantized". A satellite on the other hand can take 
any value for its angular momentum. Bohr postulated 
that the angular momentum, and thus the energy are 
quantized, and that an electron can exist in the 
atom only in states with those energies. Furthermore 
he posultated that an electron can jump between those 
states. If it jumps from a higher energy to a lower 
energy state, it emits the energy difference between 
the two states as a package of light, called a "photon". 
It it receives or absorbs a photon of exactly that 
energy difference, it jumps from the lower to the 
higher energy state. Bohr's model was very accurate 
in explaining the observed energy levels of the hydrogen 
atom, and thus introduced the idea of quantum physics, 
but it failed badly in predicting energy levels of 
atoms with more than one electron. His model is also 
very unsatisfactory in explaining many other phenomena. 
It left many questions unanswered. For example, what happens 
if two electrons in an atom come very close to each other? 
In the case of two satellites, they could send each other 
to very different orbits, but that does not always happens 
in an atom. Because all of this, physicists have discarded 
Bohr's model. Electrons are much better described in modern quantum 
mechanics as waves, rather than as particles orbiting around 
an atom with a certain speed. Still today Bohr's model can 
give some insights on how electrons in atoms behave, 
but one has to remember its many limitations. 

You can find the math needed in the Bohr model in any 
first year undergraduate physics course that treat the Bohr 
atom model. 

With the above in mind, I answer your questions directly. 
If I give a satellite a package of energy to increase its speed, 
does it jump to a higher orbit?: If you change the direction 
of its velocity, many things can happen, including that the 
satellite can fall to Earth. If you don't change the 
direction of its velocity, and only the magnitude of its 
velocity, yes, you change its orbit to one with higher energy. 
However rembemer that orbits can have variable height. 
Satellite orbits are ellipses. At its highest point the speed 
of the satellite is lowest and at its lowest point its 
speed is highest. 

Does the math for satellite height, speed and mass 
work for electrons? According to Bohr's theory it does work for
the hydrogen atom. But remember that Bohr's theory "quantizes" 
heights, speeds, energies and momenta with the condition that 
mvr=n times hbar, with n=1,2,3... This is the only additional 
mathematical condition that the Bohr model needs. Physical 
quantities are not quantized for a satellite, but they are continuous. 
According to modern quantum mechanics, the math for satellites 
does NOT work for electrons, and experimental observations 
confirm this assertion. 

Does a spinning satellite change this math?
To a first approximation it does not, because you can 
consider a satellite as a particle since it is very small 
compared to Earth. It you consider more accurate 
approximations, it changes a little the equations of 
motion. A spinning satellite can alter its orbit a little 
because it can exchange some angular momentum with the 
Earth if it is not perfectly round and is heavier in 
one side. That's why large satellites like the Space Station 
need continuous guidance. Electrons on the other hand 
don't really behave like this. In fact we don't know 
exactly how an electron is made, whether it has "parts", 
structure, etc. At some point physicists thought that an 
electron can spin, and when they tried to measure its spin, 
a big discovery was made. Electrons do have spin, but not in 
the normal sense of a spinning top. The electron spin 
alters its motion in the atom in a far more radical way 
than a spinning satellite can alter its motion around Earth. 

Vladimir Escalante Ramirez.

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