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M1L1h_CQ1.txt
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M1L1h_CQ1.txt
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#
# File: content-mit-8-421-1x-subtitles/M1L1h_CQ1.txt
#
# Captions for 8.421x module
#
# This file has 62 caption lines.
#
# Do not add or delete any lines.
#
#----------------------------------------
Let me make a note.
It's one of the many notes I will
make in this course about factors of two.
There are factors of 2.
If you miss it, you qualitatively miss the physics,
and let me in that context by talking about precession
frequencies and magnetic moment, explain
a factor of 2, which is related to the G
factor of the electron.
So if we have the electron which has spin of 1/2, in units
of the Bohr magnetron, what is a magnetic moment
of the electron?
1/2, 1 or 2?
What is the magnetic moment of the electron?
1/2, 1 or 2?
I should have a clicker question on that,
and no it's 1, 1 Bohr magnetron.
And then we sort of show the level structure of it.
You have-- this is zero energy-- You have spin up,
and you have spin down.
The difference is 2.8 megahertz per Gauss,
and if you ask what is the precession
frequency of an electron in a magnetic field,
it's 2.8 megahertz if the field is 1 Gauss,
and if you want to drive the rotation,
if you want to change the precession angle-- we'll
talk about that in great detail--
you better drive the system at 2.8 megahertz.
But 2.8 megahertz is the difference of plus 1.4
and minus 1.4, and therefore the energy
of the electron in a magnetic field
is either plus or minus 1.4 megahertz per Gauss,
and 1.4 is 1 Bohr magneton.
The magnetic moment of the electron is 1 Bohr magneton.
So precesses at 2.8.
OK, but let us contrast this with a classical current
distribution, which has 1 unit over h bar, which
means the magnetic moment is 1 Bohr magneton,
exactly as the electron has.
Well, quantum mechanically means it has three different level,
minus 1, 0 and 1, because it has one unit of angular momentum.
Since the system has one Bohr magneton, when
the system stands up or stands down,
the difference between spin up and spin down
is 2.8 megahertz per Gauss.
OK, my question now is, what is the precession frequency
of this classical charge distribution, which is 1 unit h
bar of angular momentum, and I've just
shown you the level structure.
If you now create a wave packet of those three levels, which
means wave packets of the three levels
means you have this spin which points in one direction.
What is the precession frequency of that system?
So let me give you three choices.
2.4, 1.4, with .0 megahertz per Gauss,
so please vote for A, B, or C.