MadSci Network: Physics Query:

### Re: what is the speed that the electrons and protrons spin?

Date: Wed Nov 15 03:57:51 2000
Posted By: Vladimir Escalante-Ramírez, Faculty, Institute of Astronomy, National University of Mexico
Area of science: Physics
ID: 973106652.Ph
Message:
```
In your question you did not explained what you understand
by "spin". This is important because physicists sometimes
have very definite meanings for words that people use very
loosely every day. I will understand here that you mean
by "spin" the rate at which a particle revolves around another
particle. I'll come later to a different, but no less interesting
meaning of the word "spin" in quantum physics.

Imagine a satellite revolving
around the Earth. The satellite does not fall to the Earth
because it is revolving around the Earth with enough speed and
there is nothing to stop it. The gravitational
attraction of the Earth is not enough to bring it down, and
only keeps it going around in an orbit.

The Danish physicist Niels Bohr imagined the above picture
for an electron revolving around the nucleus of an atom in 1913.
Since the electron is a particle with a negative charge, and
the nucleus of an atom has positive charge, the electron must
be revolving around the nucleus in order not to fall upon it.
He added one condition that makes it very different from the case
of the satellite around the Earth. The electron only has certain
permitted orbits around the nucleus. Satellites on the other hand
can have orbits at any distance from Earth. His theory was
very successful in explaining some observed facts of the hydrogen
atom. His theory predicts that the electron will revolve in
its lowest permitted orbit around
the hydrogen nucleus (which is a proton) at the speed of

2.2 X 10^8 centimeters per second

(here 10^8 means 10 to the
eight power, that's 100000000 or 100 million). Notice that
this is about one percent of the speed of light, which is
a very high speed for human standards indeed! The electron
can have higher, slower permitted orbits around the
proton with a speed given by

2.2 X 10^8 / n  centimeters per second

where n in the above formula is any integer you like from 1 to
infinity. The higher the value of n, the higher the orbit of
the electron in the atom. The formula reflects the fact that
according to Bohr's theory not all orbits are possible. Only
those for which the speed is given by the above formula.

The number of turns per second of the electron around the
nucleus is given by a similar formula:

6.6 X 10^15 / n^3 turns per second

(that's 6.6 times 10 to the fifteenth power divided by the cube
of n), where again n is any integer from 1 to infinity.

Now you may wonder that if n is really high we could have
electrons going very slowly, and maybe catch one. It turns
out that if an electron is in a very high orbit (n very large)
it will be most likely stripped from the atom by any jolt
that the atom suffers.

The Bohr theory suffers from many severe problems.
For example, it cannot explain atoms with more that
one electron, and leaves many questions unanswered, like
"What happens if two electrons in an atom collide?
What if I send an electron straight into the nucleus?"
Bohr's theory is still useful to help us understand
certain facts of the atom, but generally speaking
is quite unsatisfactory, and because of that,
physicists no longer use it for serious calculations.
Physics has demonstrated that looking at electrons
and protons as particles often leads to contradictions.
Nobody has seen an electron or a proton yet, so we don't
really know what they are or whether they are
spinning around something.

Protons don't usually revolve around other particles because
they are too heavy. Instead lighter particles like electrons
revolve around protons. When protons revolve around something,
it is because they are part of molecules
that rotate around their own center. At very low temperatures,
the protons in a hydrogen molecule revolve around each other
7 X 10^12 times per second, which correspond to a speed
of 200000 centimeters per second. Much slower than the
electrons around the nucleus of an atom.

So I promised to explain what physicists actually understand by
the spin of an electron. When physicists were trying
to understand how electrons behave, they came to the conclusion that
electrons could be something that spin, like a top or a
football in the air. It turned out that electrons, and
protons are not really balls or tops or whatever, but
they nevertheless behave as if they were spinning at a certain
rate. That rate is called the spin and all protons and
electrons have the same value of spin, but it turns out that
this spin really cannot be described with a speed of rotation.

Vladimir Escalante Ramirez

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