de Broglie wavelengths

The title says it all. This is for established factual (we hope) things.

de Broglie wavelengths

Postby Doug Coulter » Fri Dec 06, 2013 8:16 pm

Oops! Jumped the gun and didn't get my e-24 on the amu in grams number. Thus, the below verbiage is wrong. When I fix that bug, things work out more to our favor. Being honest, I'll leave the wrong stuff up and just tell you - and give you the right stuff.

This one is quite a bit more encouraging, not to mention, more correct. Good news!
debroglie2.zip
bug fixed
(889 Bytes) Downloaded 419 times

The only change was for the amu in grams, adding that correct exponent.

Sample output, now (thermal speed):
Code: Select all
doug@doug-laptop:~$ debroglie
Electron or amu (e or a), A>
Number of amu?>2
Volts?>.025
DeBroglie wavelength for nucleus at .025 volts is:1.28506925036876e-08 cm
Approximate physical diameter for nucleus of 2 amu is: 3.45218366873571e-13 cm
done


and for 50kv:
Code: Select all
doug@doug-laptop:~$ debroglie
Electron or amu (e or a), A>
Number of amu?>2
Volts?>50000
DeBroglie wavelength for nucleus at 50000 volts is:9.08681181230062e-12 cm
Approximate physical diameter for nucleus of 2 amu is: 3.45218366873571e-13 cm
done


So, here, we in fact see a large increase in effective size due to the de Broglie wavefunction - about a factor of 30 at 50kv.
I *thought* that might be the case, but went with the (wrong) numbers below...now I know better.



/////// right idea below, but wrong mass constant for amu...see above, the conclusions below were just plain wrong.

Due to some other questions I had about the relative scales of things, I decided to write a short/dirty perl progrqam based on the books I have and existing data to calculate de Broglie wavelengths of either electrons, or nuclei. Seems every book has all this, but sometimes (all too often) they mix units and so forth...at least a few of the books give worked examples so I could test if I was doing it right, and this allowed me to write the program correctly and allow you to use the familiar CGS units, not have to figure out Planck's constant's units, remember things to n decimals and so forth. Very handy...I got most of my numbers from here: http://en.wikipedia.org/wiki/Centimetre ... m_of_units
Except for the size of one (or more) nucleons, which I got from Halliday...it seems that different ways of measuring those result in a number of anywhere from 1.1 to 1.5x e-13..at least when Halliday published them. It's probably still the case, but what I show is, heck, for us, it doesn't matter much anyway...

In particular, the question I was trying to answer for myself was "does the de Broglie wavelength help us any in fusion - is it big enough to make the deuteron look bigger than it does in say, high energy neutron scattering experiments?". Sadly, nope, not even close...but the program is still useful to get a feel for this quantum uncertainty stuff - and the de Broglie limit DOES tell you how fine, in theory, you could "aim" something at something else, with all the uncertainy stuff taken into account. I DID check this against various worked out examples from the old physics books.

Some sample runs:
Electrons at 100 eV:
Code: Select all
doug@doug-laptop:~$ debroglie
Electron or amu (e or a), A>e
Volts?>100
Electron wavelength for 100 volts is:1.22685033152376e-08 cm
done
doug@doug-laptop:~$


roughly thermal deuterons:
Code: Select all
doug@doug-laptop:~$ debroglie
Electron or amu (e or a), A>a
Number of amu?>2
Volts?>.025
DeBroglie wavelength for nucleus at .025 volts is:1.28506925036876e-20 cm
Approximate physical diameter for nucleus of 2 amu is: 3.45218366873571e-13 cm
done
doug@doug-laptop:~$

As you can see, any hopes de Broglie helps us out by making deuterons look bigger due to their wave/particle duality is therefore dashed. It gets worse...
Here's a run with 50kv, which only assumes 25kv per deuteron if they're hitting head on...
Code: Select all
doug@doug-laptop:~$ debroglie
Electron or amu (e or a), A>a
Number of amu?>2
Volts?>50000
DeBroglie wavelength for nucleus at 50000 volts is:9.08681181230062e-24 cm
Approximate physical diameter for nucleus of 2 amu is: 3.45218366873571e-13 cm
done
doug@doug-laptop:~$

> 3*10e10 dufferebce - no help from this quarter, we might assume.


Here's the (very fast and sloppy, I admit) perl code, which I'll also attach as a zip for those who have perl (anyone who goes and gets it, or runs linux or mac os already has it).
Code: Select all
#!/usr/bin/perl -w
use strict;

# very quick and dirty perl for calculating debroglie wavelengths of stuff
# also output physical size of nuclei when stationary (0 deg K, I suppose)
# gnu license v2 - share and enjoy, improve if you want to, and share back, please.
# dcfusor@gmail.com  12/6/2013

my $h = 6.62606885e-27; # planck in CGS units (all these from Wikipedia, 2013)
my $amu = 1.660538782; # amu in grams !!!@@@!!! BUG!  add e-24 to this number!  Protons don't weigh over a gram!
my $mE = 9.10938215e-28; # mass of electron, grams
my $e = 4.80320427e-10; # unit charge in stat-coulomb
my $r0 = 1.37e-13; # radius/nucleon roughly (from Halliday, old neutron scattering number)
my $input; # from console
my $wavelength; # debroglie wavelength
my $volts;
my $weight;
my $radius;
my $diameter;

print ("Electron or amu (e or a), A>");
$input = lc <>;
chomp $input;
if ($input eq 'e')
{
print "Volts?>";
$volts = <>;
chomp $volts;

$wavelength = $h/sqrt($mE*$e*$volts/150);

print "Electron wavelength for $volts volts is:$wavelength cm\n"

}
else
{
print "Number of amu?>";
$input = <>;
chomp $input;
$weight = $amu * $input; # now have in grams

print "Volts?>";
$volts = <>;
chomp $volts;

$wavelength = $h/sqrt($weight*$e*$volts/150);
print "DeBroglie wavelength for nucleus at $volts volts is:$wavelength cm\n";
$radius = $r0 * ($input**.33333333);
$diameter = $radius * 2;

print "Approximate physical diameter for nucleus of $input amu is: $diameter cm \n";
}

print "done\n"

debroglie.zip
Perl program - has a bug, fixed and re-released at the top of post
(832 Bytes) Downloaded 406 times
Posting as just me, not as the forum owner. Everything I say is "in my opinion" and YMMV -- which should go for everyone without saying.
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Doug Coulter
 
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Location: Floyd county, VA, USA

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