This is absolutely correct. Radian is in fact just another symbol for 1.
Thus : 1 rad = 1
From the official SI documentation
(http://www.bipm.org/en/si/si_brochure)(section 2.2 - table 3) :
"The radian and steradian are special names for the number one that
may be used to convey information about the quantity concerned. In
practice the symbols rad and sr are used where appropriate, but the
symbol for the derived unit one is generally omitted in specifying the
values of dimensionless quantities."
Marc
Quoting Ian Tickle <i.tic...@astex-therapeutics.com>:
Back to the original problem: what are the units of B and
<u_x^2>? I haven't been able to work that out. The first
wack is to say the B occurs in the term
Exp( -B (Sin(theta)/lambda)^2)
and we've learned that the unit of Sin(theta)/lamda is 1/Angstrom
and the argument of Exp, like Sin, must be radian. This means
that the units of B must be A^2 radian. Since B = 8 Pi^2 <u_x^2>
the units of 8 Pi^2 <u_x^2> must also be A^2 radian, but the
units of <u_x^2> are determined by the units of 8 Pi^2. I
can't figure out the units of that without understanding the
defining equation, which is in the OPDXr somewhere. I suspect
there are additional, hidden, units in that definition. The
basic definition would start with the deviation of scattering
points from the Miller planes and those deviations are probably
defined in cycle or radian and later converted to Angstrom so
there are conversion factors present from the beginning.
I'm sure that if the MS sits down with the OPDXr and follows
all these units through he will uncover the units of B, 8 Pi^2,
and <u_x^2> and the mystery will be solved. If he doesn't do
it, I'll have to sit down with the book myself, and that will
make my head hurt.
Hi Dale
A nice entertaining read for a Sunday afternoon, but I think you can
only get so far with this argument and then it breaks down, as evidenced
by the fact that eventually you got stuck! I think the problem arises
in your assertion that the argument of 'exp' must be in units of
radians. IMO it can also be in units of radians^2 (or radians^n where n
is any unitless number, integer or real, including zero for that
matter!) - and this seems to be precisely what happens here. Having a
function whose argument can apparently have any one of an infinite
number of units is somewhat of an embarrassment! - of course that must
mean that the argument actually has no units. So in essence I'm saying
that quantities in radians have to be treated as unitless, contrary to
your earlier assertions.
So the 'units' (accepting for the moment that the radian is a valid
unit) of B are actually A^2 radian^2, and so the 'units' of 8pi^2 (it
comes from 2(2pi)^2) are radian^2 as expected. However since I think
I've demonstrated that the radian is not a valid unit, then the units of
B are indeed A^2!
Cheers
-- Ian
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