How far does nuclear radiation travel from the core of an explosion?

Greetings.

The distance that fallout particles would travel depends on several
factors.  I am answering for fallout particles specifically because of
all the radiation created in consequence of a nuclear explosion, these
are the farthest travelling and longest lasting.

One of these factors is of course the size of the explosion.  Other
less obvious factors include how close the explosion occurs to the
ground.  According to Nuclearfiles.org
(http://www.nuclearfiles.org/kinuclearweapons/effectstarget.htm),
"nuclear weapons detonated at ground level generate more fallout as a
result of the large amount of ground material which is irradiated by
the explosion and thrownin the air..."  This fallout "can carry
radiation up to several hundred miles"
(http://abcnews.go.com/sections/living/DailyNews/nuclearattacks_health020604.html).

The most important factor as to how far radiation travels from the
core of explosion is the weather.  An article hosted by the Federation
of American Scientists
(http://www.fas.org/nuke/intro/nuke/radiation.htm) states that:

"Atmospheric winds are able to distribute fallout over large areas.
For example, as a result of a surface burst of a 15 Mt thermonuclear
device at Bikini Atoll on March 1, 1954, a roughly cigar-shaped area
of the Pacific extending over 500 km downwind and varying in width to
a maximum of 100 km was severely contaminated. Snow and rain,
especially if they come from considerable heights, will accelerate
local fallout."

Though not technically a nuclear explosion, the reactor meltdown at
Chernobyl in 1986 is one of the most studies instances of fallout in
world history.  Many maps of the fallout effects of Chernobyl on the
world are available at
http://www.catsm.org/missions/chernobyl_files/maps_exposure/index.htm.

So, it totally depends on the winds.  The radiation levels decrease,
of course, by distance from the event, but individual particles travel
very far indeed.  The answer to your question, as presently worded, is
"they can travel hundreds and hundreds of miles."

Now, if your question is how far does significant radiation travel
from the core of an explosion, the answer is similar (it depends on
the weather) but is much less serious as far as distance. 
http://people.smu.edu/rmonagha/fallout.html is a theoretical model for
determining individual exposure, based on the parameters of weapon
size, cloud wind speed, and distance (of a shelter) from the center of
an explosion.

Search terms: 

nuclear explosion radiation distance
://www.google.com/search?q=nuclear+explosion+radiation+distance&ie=UTF-8&oe=UTF-8
nuclear fallout "ground level"
://www.google.com/search?q=nuclear+fallout+%22ground+level%22&ie=UTF-8&oe=UTF-8
chernobyl fallout map
://www.google.com/search?q=chernobyl+fallout+map&ie=UTF-8&oe=UTF-8

Thanks for your question and thanks for using Google Answers
surajambar-ga

You havn't answered the question,  lolohank  did not ask about
fallout. Remember the so-called neutron bomb of the eighties which
relied on radiation generated by the initial blast to kill people
inside buildings and tanks.

Lolohank, in your view, have I answered your question?  If not, let me
know and I will gladly clarify further.

Kemlo, fallout particles *are* among the radioactive byproducts which
travel from the core of an explosion.  According to the Encyclopędia
Britannica, "The explosion of nuclear bombs that release radioactivity
leads to three separate types of fallout: local, tropospheric, and
stratospheric. The local fallout is due to the deposition of the
larger radioactive particles near the site of the explosion?
stratospheric fallout, made up of extremely fine particles [i.e.
radiation] in the stratosphere (above the troposphere), may continue
years after the explosion, and the distribution is nearly worldwide." 
As fas as I can tell, this is the answer that lolohank is looking for
as it is the farthest radiation is spread after a nuclear explosion.

Again, please let me know if the answer you want is for a more precise
question about the radiation generated by the initial blast.

surajambar-ga

The radiation extends out from the blast center a very great distance,
but typically the hazzard decreases as the cube of the distance, so it
is rare that anyone gets double the back ground radiation of any kind
of particle or ray more than 1000 miles from the blast center. I say
cube instead of square as the atmosphere scatters and absorbs all
radiation except nutrinos. Typically you are killed by the heat and
concussion if you are close enough to ground zero the be killed
promptly by the radiation. If you see the fire ball 50 miles away, you
have received enough radiation (gamma, Xray and hard ultraviolet) to
have at least a slightly increased cancer risk. The alpha, beta,
neutrons and other less numerious particles arrive about a second
later, so you may have time to at least lay down which will usually
reduces your exposure.
  Sur gave a good description of the radiation from fallout which is
typically far more important to the survivers than the direct
radiation from the detination, which is mostly over in one second.
 Kemlo is correct neutron bombs produce lots of deadly nuetrons, but
reduced blast damage. Does any country have a significant number of
neutron bombs or cobalt bombs? The latter produce lots of cobalt 90.  
Neil